Analyze and Sketch Function Graphs - 8th Grade Math
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What qualitative graph matches “decreases at a constant rate”?
What qualitative graph matches “decreases at a constant rate”?
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A straight line falling left to right (linear with $m<0$). Constant negative slope creates steady downward line.
A straight line falling left to right (linear with $m<0$). Constant negative slope creates steady downward line.
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Identify the slope sign when a graph falls from left to right.
Identify the slope sign when a graph falls from left to right.
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Negative slope: $m<0$. Falling lines have negative slopes.
Negative slope: $m<0$. Falling lines have negative slopes.
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Identify the slope sign when a graph rises from left to right.
Identify the slope sign when a graph rises from left to right.
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Positive slope: $m>0$. Rising lines have positive slopes.
Positive slope: $m>0$. Rising lines have positive slopes.
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What does the slope represent for a graph of $y$ versus $x$?
What does the slope represent for a graph of $y$ versus $x$?
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The rate of change: $ rac{ ext{change in }y}{ ext{change in }x}$. Slope measures steepness and direction of change.
The rate of change: $ rac{ ext{change in }y}{ ext{change in }x}$. Slope measures steepness and direction of change.
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What graphical feature shows that a relationship is nonlinear?
What graphical feature shows that a relationship is nonlinear?
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The graph is not a straight line; the slope changes. Curves or bends indicate varying rates of change.
The graph is not a straight line; the slope changes. Curves or bends indicate varying rates of change.
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What graphical feature shows that a relationship is linear?
What graphical feature shows that a relationship is linear?
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The graph is a straight line with constant slope. Linear means constant rate of change between any two points.
The graph is a straight line with constant slope. Linear means constant rate of change between any two points.
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What does it mean for a function to be constant on an interval in a graph?
What does it mean for a function to be constant on an interval in a graph?
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As $x$ changes, $y$ stays the same (a horizontal segment). Horizontal line has zero slope, so $y$ doesn't change.
As $x$ changes, $y$ stays the same (a horizontal segment). Horizontal line has zero slope, so $y$ doesn't change.
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What does it mean for a function to be decreasing on an interval in a graph?
What does it mean for a function to be decreasing on an interval in a graph?
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As $x$ increases, $y$ decreases (the graph falls left to right). Falling graph means negative change in $y$ as $x$ grows.
As $x$ increases, $y$ decreases (the graph falls left to right). Falling graph means negative change in $y$ as $x$ grows.
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What does it mean for a function to be increasing on an interval in a graph?
What does it mean for a function to be increasing on an interval in a graph?
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As $x$ increases, $y$ increases (the graph rises left to right). Rising graph means positive change in $y$ as $x$ grows.
As $x$ increases, $y$ increases (the graph rises left to right). Rising graph means positive change in $y$ as $x$ grows.
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What qualitative graph matches “increases at a constant rate”?
What qualitative graph matches “increases at a constant rate”?
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A straight line rising left to right (linear with $m>0$). Constant positive slope creates steady upward line.
A straight line rising left to right (linear with $m>0$). Constant positive slope creates steady upward line.
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Which interval shows the function increasing for points $(1,2)$, $(3,5)$, $(6,4)$?
Which interval shows the function increasing for points $(1,2)$, $(3,5)$, $(6,4)$?
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Increasing on $1\le x\le 3$. $y$ goes from 2 to 5 as $x$ goes from 1 to 3.
Increasing on $1\le x\le 3$. $y$ goes from 2 to 5 as $x$ goes from 1 to 3.
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What is the $y$-intercept on a graph, in words and notation?
What is the $y$-intercept on a graph, in words and notation?
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The value of $y$ when $x=0$; point $(0,b)$. Where the graph crosses the vertical axis.
The value of $y$ when $x=0$; point $(0,b)$. Where the graph crosses the vertical axis.
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What is the $x$-intercept on a graph, in words and notation?
What is the $x$-intercept on a graph, in words and notation?
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The value of $x$ when $y=0$; point $(a,0)$. Where the graph crosses the horizontal axis.
The value of $x$ when $y=0$; point $(a,0)$. Where the graph crosses the horizontal axis.
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Identify the $y$-intercept of the line through $(0,-2)$ and $(3,4)$.
Identify the $y$-intercept of the line through $(0,-2)$ and $(3,4)$.
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$y$-intercept is $-2$ (point $(0,-2)$). The line passes through $(0,-2)$.
$y$-intercept is $-2$ (point $(0,-2)$). The line passes through $(0,-2)$.
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Which interval shows the function decreasing for points $(1,2)$, $(3,5)$, $(6,4)$?
Which interval shows the function decreasing for points $(1,2)$, $(3,5)$, $(6,4)$?
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Decreasing on $3\le x\le 6$. $y$ goes from 5 to 4 as $x$ goes from 3 to 6.
Decreasing on $3\le x\le 6$. $y$ goes from 5 to 4 as $x$ goes from 3 to 6.
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Is the line through $(0,3)$ and $(4,1)$ increasing or decreasing?
Is the line through $(0,3)$ and $(4,1)$ increasing or decreasing?
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Decreasing, since $m=\frac{1-3}{4-0}=-\frac{1}{2}$. Negative slope means the line falls.
Decreasing, since $m=\frac{1-3}{4-0}=-\frac{1}{2}$. Negative slope means the line falls.
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Which is steeper: line $A$ with slope $2$ or line $B$ with slope $\frac{1}{2}$?
Which is steeper: line $A$ with slope $2$ or line $B$ with slope $\frac{1}{2}$?
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Line $A$ is steeper because $|2|>|\frac{1}{2}|$. Compare absolute values of slopes for steepness.
Line $A$ is steeper because $|2|>|\frac{1}{2}|$. Compare absolute values of slopes for steepness.
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What qualitative graph matches “starts high, decreases quickly, then levels off”?
What qualitative graph matches “starts high, decreases quickly, then levels off”?
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A decreasing curve that flattens (slope negative, $|m|$ shrinking). Rapid decrease followed by gradual leveling.
A decreasing curve that flattens (slope negative, $|m|$ shrinking). Rapid decrease followed by gradual leveling.
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What does it mean if a graph becomes less steep (flattens) as $x$ increases?
What does it mean if a graph becomes less steep (flattens) as $x$ increases?
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The rate of change is decreasing; $y$ changes slower per $1$ in $x$. Flatter slope means slower rate of change.
The rate of change is decreasing; $y$ changes slower per $1$ in $x$. Flatter slope means slower rate of change.
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What does it mean if a graph becomes steeper as $x$ increases?
What does it mean if a graph becomes steeper as $x$ increases?
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The rate of change is increasing; $y$ changes faster per $1$ in $x$. Steeper slope means faster rate of change.
The rate of change is increasing; $y$ changes faster per $1$ in $x$. Steeper slope means faster rate of change.
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What does a slope of $0$ mean about the graph and the relationship?
What does a slope of $0$ mean about the graph and the relationship?
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The graph is horizontal; $y$ is constant as $x$ changes. No slope means no vertical change.
The graph is horizontal; $y$ is constant as $x$ changes. No slope means no vertical change.
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What does a positive slope mean about the relationship between $x$ and $y$?
What does a positive slope mean about the relationship between $x$ and $y$?
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Positive relationship: as $x$ increases, $y$ increases. Both variables move in the same direction.
Positive relationship: as $x$ increases, $y$ increases. Both variables move in the same direction.
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Which option describes a linear graph: A) curve B) straight line C) zigzag with corners?
Which option describes a linear graph: A) curve B) straight line C) zigzag with corners?
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B) Straight line. Linear graphs are always straight lines.
B) Straight line. Linear graphs are always straight lines.
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What qualitative change occurs if a graph switches from falling to rising at one point?
What qualitative change occurs if a graph switches from falling to rising at one point?
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It changes from decreasing to increasing at a turning point (minimum). A valley where direction reverses.
It changes from decreasing to increasing at a turning point (minimum). A valley where direction reverses.
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Identify the intervals of increase for a V-shape with vertex at $(0,0)$ opening upward.
Identify the intervals of increase for a V-shape with vertex at $(0,0)$ opening upward.
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Increasing for $x>0$ (and decreasing for $x<0$). V-shape rises on the right side of vertex.
Increasing for $x>0$ (and decreasing for $x<0$). V-shape rises on the right side of vertex.
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