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SSAT Upper Level Math : How to find transformation for an analytic geometry equation

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Example Questions

Example Question #461 : Ssat Upper Level Quantitative (Math)

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x|+3

y = | x-3|

y = | x+3|

$y = \left | \frac{1}{3}x \right |$

y = |3x|

Correct answer:

y = |3x|

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the same as the above graph, except that each -coordinate is paired with the -coordinate three times that with which it is paired in the above graph. Therefore, the equation graphed is

$y = 3 \cdot |x|$

y = |3x|

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Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation $y= x^{2}+ 2x - 17$ is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?

Possible Answers:

$y= x^{2}+8x -2$

$y= x^{2}-4x -14$

$y= 2 x^{2}+ 4x - 34$

$y= x^{2}+ 2x - 20$

$y= x^{2}+ 2x - 14$

Correct answer:

$y= x^{2}-4x -14$

Explanation:

The graph of a function y = f(x) shifted right three units is the graph of y = f(x-3) . In this graph, $f(x)= x^{2}+ 2x - 17$ , so the graph formed by the transformation is

$f(x-3)= \left (x-3 \right ) ^{2}+ 2 (x-3) - 17$

$f(x-3)= x^{2}-6x+9+ 2x-6 - 17$

$f(x-3)= x^{2}-6x+ 2x+9-6 - 17$

$f(x-3)= x^{2}-4x -14$

The correct equation is $y= x^{2}-4x -14$ .

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Example Question #191 : Coordinate Geometry

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the origin, what will the equation of the resulting graph be?

Possible Answers:

y = 2x^2 - 5x - 17

y = 2x^2 +5x +17

y =- 2x^2 +5x +17

y = 2x^2+ 5x-17

y =- 2x^2 -5x +17

Correct answer:

y =- 2x^2 +5x +17

Explanation:

The reflection of the graph of the equation y = f(x) about the origin is the graph of the equation -y = f(-x) , so replace with and with :

y = 2x^2 + 5x - 17

becomes

- y = 2 (-x) ^2 + 5 (-x) - 17

- y = 2 x^2 -5x - 17

-(-y) = - (2 x^2 -5x - 17)

y= - 2 x^2 +5x +17

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Example Question #192 : Coordinate Geometry

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the -axis, what will the equation of the resulting graph be?

Possible Answers:

y =- 2x^2 +5x +17

y = 2x^2 +5x +17

y =- 2x^2 -5x +17

y = 2x^2+ 5x-17

y = 2x^2 - 5x - 17

Correct answer:

y =- 2x^2 -5x +17

Explanation:

The reflection of the graph of the equation y = f(x) about the -axis is the graph of the equation -y = f(x) , so replace with :

y = 2x^2 + 5x - 17

becomes

-y = 2x^2 + 5x - 17

$-(-y) = - (2x^{2 }+ 5x - 17)$

y =- 2x^2 -5x +17

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Example Question #193 : Coordinate Geometry

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the -axis, what will the equation of the resulting graph be?

Possible Answers:

y = 2x^2+ 5x-17

y =- 2x^2 +5x +17

y =- 2x^2 -5x +17

y = 2x^2 - 5x - 17

y = 2x^2 +5x +17

Correct answer:

y = 2x^2 - 5x - 17

Explanation:

The reflection of the graph of the equation y = f(x) about the -axis is the graph of the equation y = f(-x) , so replace with :

y = 2x^2 + 5x - 17

becomes

y = 2 (-x) ^2 + 5 (-x) - 17

y = 2 x^2 -5x - 17

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Example Question #194 : Coordinate Geometry

If the graph of the equation y = |x+3| - 5 is reflected about the origin, what will the equation of the resulting graph be?

Possible Answers:

y =- |x+3| + 5

y=- |x-3| +5

y =- |x+3| - 5

y =- |x-3| - 5

None of the other responses gives a correct answer.

Correct answer:

y=- |x-3| +5

Explanation:

The reflection of the graph of the equation y = f(x) about the origin is the graph of the equation -y = f(-x) , so replace with and with :

y = |x+3| - 5

becomes

-y = |-x+3| - 5

-(-y) =-( |-x+3| - 5)

y=- |-x+3| +5

The absolute values of two expressions that are each other's opposites are equal, so |-x+3| is equivalent to |x-3| . The expression can be rewritten as

y=- |x-3| +5 .

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Example Question #474 : Ssat Upper Level Quantitative (Math)

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x-3| - 5

y = |x+5| - 3

y = |x-5| + 3

y = |x+5| + 3

y = |x+3| + 5

Correct answer:

y = |x+5| + 3

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted right five units and upward three units. The graph of any function y = f(x) shifted right five units and upward three units is y = f(x+5)+3 , so the correct response is y = |x+5| + 3 .

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Example Question #471 : Ssat Upper Level Quantitative (Math)

If the graph of the equation $y= x^{2}+ 3x - 5$ is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?

Possible Answers:

$y = x ^{2}-11x+23$

$y = x ^{2}+17x+65$

$y=\frac{1}{7} x^{2}+ \frac{3}{7}x - \frac{5}{7}$

$y= x^{2}+ 3x+2$

$y= x^{2}+ 3x - 12$

Correct answer:

$y= x^{2}+ 3x - 12$

Explanation:

The graph of a function y = f(x) shifted downward seven units is the graph of y = f(x) -7 . In this graph, $f(x)= x^{2}+ 3x - 5$ , so the graph formed by the transformation is that of the equation

$y = ( x^{2}+ 3x - 5)-7$

$y = x^{2}+ 3x -12$

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Example Question #195 : Coordinate Geometry

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x-2|

y =|x|+2

y = |2x|

y = |x+2|

y =|x|-2

Correct answer:

y = |x-2|

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted right two units. The graph of y = f(x) shifted right two units is y = f(x-2) , so the correct response is y = |x-2| .

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Example Question #196 : Coordinate Geometry

Function 2

What equation is graphed in the above figure?

Possible Answers:

$y = \left \lceil x\right \rceil - 3$

$y = \left \lfloor x\right \rfloor - 4$

$y = \left \lfloor x\right \rfloor - 3$

$y = \left \lfloor x\right \rfloor +3$

$y = \left \lceil x\right \rceil - 4$

Correct answer:

$y = \left \lfloor x\right \rfloor - 4$

Explanation:

The greatest integer function, or floor function, $y = \left \lfloor x\right \rfloor$ , pairs each value of with the greatest integer less than or equal to . Its graph is below.

Floor function

The given graph is the above graph shifted downward four units. The graph of any function y = f(x) shifted downward four units is y = f(x) - 4 , so the given graph corresponds to equation $y = \left \lfloor x\right \rfloor - 4$ .

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SSAT Upper Level Math : How to find transformation for an analytic geometry equation

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #461 : Ssat Upper Level Quantitative (Math)

Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

Example Question #191 : Coordinate Geometry

Example Question #192 : Coordinate Geometry

Example Question #193 : Coordinate Geometry

Example Question #194 : Coordinate Geometry

Example Question #474 : Ssat Upper Level Quantitative (Math)

Example Question #471 : Ssat Upper Level Quantitative (Math)

Example Question #195 : Coordinate Geometry

Example Question #196 : Coordinate Geometry

All SSAT Upper Level Math Resources

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