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Common Core: 8th Grade Math : Understand Functions: CCSS.Math.Content.8.F.A.1

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #4 : Finding Roots

Solve the equation:

$\small 13 = x^2-12x$

Possible Answers:

$\small \left \{0\right\}$

$\small \left \{-1, 13 \right \}$

$\small \left \{-13, 1\right \}$

$\small \left \{ 1, 2 \right \}$

$\small \left \{ 2, 4\right \}$

Correct answer:

$\small \left \{-1, 13 \right \}$

Explanation:

To solve the quadratic equation, $\small 13= x^{2} -12x$ , we set the equation equal to zero and then factor the quadratic, $\small (x-13)(x+1)=0$ . Because these expressions multiply to equal 0, then it must be that at least one of the expressions equals 0. So we set up the corresponding equations x-13=0 and x+1=0 to obtain the answers x=13 and x=-1 .

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Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

Solve for :

$x^{2}+12x+35=0$

Possible Answers:

x=3,15

x=-5,-7

x=7,9

The solution is undefined.

x=-5,-9

Correct answer:

x=-5,-7

Explanation:

To factor this equation, first find two numbers that multiply to 35 and sum to 12. These numbers are 5 and 7. Split up 12x using these two coefficients:

x^2 + 7x+5x+35=0

x(x+7)+5(x+7)=0

(x+5)(x+7)=0

x=-5,-7

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Example Question #2 : Understand Functions: Ccss.Math.Content.8.F.A.1

Solve for :

$3x^{2}-18x+24=0$

Possible Answers:

$x=-6,\,1$

$x=-1,\,-6$

$x=-2,\,4$

$x=2,\,4$

$x=2,\,3$

Correct answer:

$x=2,\,4$

Explanation:

To find , we must factor the quadratic function:

$3x^{2}-18x+24=0$

$3(x^{2}-6x+8)=0$

3(x-4)(x-2)=0

$x-4=0\, and \, x-2=0$

$x=4\,and\,2$

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Example Question #3 : Understand Functions: Ccss.Math.Content.8.F.A.1

Solve for :

$2x^{2}-10x-28=0$

Possible Answers:

$x=-2\,and\,x=7$

$x=2\,and\,x=-5$

$x=-2\,and\,x=5$

$x=-1\,and\,x=5$

$x=2\,and\,x=-7$

Correct answer:

$x=-2\,and\,x=7$

Explanation:

To find , we want to factor the quadratic function:

$2x^{2}-10x-28=0$

$2(x^{2}-5x-14)=0$

2(x-7)(x+2)=0

$x-7=0\,and\,x+2=0$

$x=7\:and\:-2$

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Example Question #4 : Understand Functions: Ccss.Math.Content.8.F.A.1

Which of the following equations represents a one-to-one function:

A) y = 3

B) y = 3x +5

$C) y = 3x^{2}-5$

$D) y^{2}= x^{2} - 5$

E) x = -3

Possible Answers:

Correct answer:

Explanation:

Only equation B maps each value of into a unique value of and in a similar way each and every value of maps into one and only one value of .

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Example Question #5 : Understand Functions: Ccss.Math.Content.8.F.A.1

$f(x) = \frac{x^{4}-x+\sqrt[3]{x}}{x^{x}+3x}$

Find f(1) .

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

Undefined

Correct answer:

$\frac{1}{4}$

Explanation:

This question demonstrates that complicated functions are not complicated at every point.

To solve the function at x=1, all that is necessary is familiarity with the operations used.

$f(1) = \frac{1^{4}-1+\sqrt[3]{1}}{1^{1}+3(1)}$

$= \frac{1-1+1}{1+3}$

$=\frac{1}{4}$

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Example Question #6 : Understand Functions: Ccss.Math.Content.8.F.A.1

Define $f(x) = x^{2} - 4x + 7$ .

Evaluate f(6) .

Possible Answers:

f(6) = 199

f(6) = 19

f(6) = -132

f(6) = 5

f(6) = 121

Correct answer:

f(6) = 19

Explanation:

To evaluate f(6) substitute six in for every x in the equation.

$f(x) = x^{2} - 4x + 7$

$\\f(6) = 6^{2} - 4 \cdot 6 + 7 \\f(6)= 36 - 24 + 7\\f(6) = 12 + 7 \\f(6)= 19$

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Example Question #7 : Understand Functions: Ccss.Math.Content.8.F.A.1

Define g(x )= 3x - 13

Which of the following is equivalent to g(x+ 6 ) ?

Possible Answers:

3x+ 7

3x-5

3x+ 5

3x- 7

Correct answer:

3x+ 5

Explanation:

To solve this problem replace every x in g(x) with x+6 .

g(x )= 3x - 13

Therefore,

g(x+ 6 )= 3(x+ 6 ) - 13

$= 3\cdot x+ 3 \cdot 6 - 13$

= 3 x+ 18- 13

= 3 x+ 5

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Example Question #8 : Understand Functions: Ccss.Math.Content.8.F.A.1

Select the table that properly represents a function.

Possible Answers:

Screen shot 2016 03 14 at 8.52.16 am

Screen shot 2016 03 14 at 8.53.45 am

Screen shot 2016 03 14 at 8.52.05 am

Screen shot 2016 03 14 at 8.53.16 am

Correct answer:

Screen shot 2016 03 14 at 8.52.05 am

Explanation:

Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.

In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:

Screen shot 2016 03 14 at 8.52.05 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 8.52.56 am

Screen shot 2016 03 14 at 8.53.29 am

Screen shot 2016 03 14 at 8.53.57 am

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Example Question #9 : Understand Functions: Ccss.Math.Content.8.F.A.1

Select the table that properly represents a function.

Possible Answers:

Screen shot 2016 03 14 at 9.55.39 am

Screen shot 2016 03 14 at 9.56.08 am

Screen shot 2016 03 14 at 9.56.36 am

Screen shot 2016 03 14 at 9.54.52 am

Correct answer:

Screen shot 2016 03 14 at 9.54.52 am

Explanation:

In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:

Screen shot 2016 03 14 at 9.54.52 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 9.55.50 am

Screen shot 2016 03 14 at 9.56.24 am

Screen shot 2016 03 14 at 9.56.49 am

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Understand Functions: CCSS.Math.Content.8.F.A.1

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #4 : Finding Roots

Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #2 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #3 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #4 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #5 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #6 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #7 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #8 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #9 : Understand Functions: Ccss.Math.Content.8.F.A.1

All Common Core: 8th Grade Math Resources

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