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Algebra 1 : Functions and Lines

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Example Question #81 : Functions And Lines

If f(x) = 2x^2 - 4x +1 , then which of the following is equivalent to f(t + 2) ^?

Possible Answers:

2t^2 + 4t + 1

2t^2 + 4t + 5

t^2 - 4t + 1

2t^2 + 4t + 17

t^2 + 4t + 1

Correct answer:

2t^2 + 4t + 1

Explanation:

Plug in (t+2) for .

f(x) = 2x^2 - 4x +1

x=t+2

f(t+2) = 2(t+2)^2 - 4(t+2) +1

FOIL the squared term and distribute -4:

2(t^2+2t+2t+4)-4t-2+1

Distribute the 2:

2t^2+8t+8-4t-2+1

Combine like terms:

2t^2 + 4t + 1

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Example Question #81 : Functions And Lines

Define g (x) = 5x +7 .

If g (A) = 24 , evaluate .

Possible Answers:

A = 11.8

A = 3.4

A=127

A=113

A=6.2

Correct answer:

A = 3.4

Explanation:

Plug in as if it were a constant, and then solve for its value:

g (A) = 5A +7 = 24

5A +7 - 7 = 24-7

5A = 17

$5A \div 5 = 17\div 5$

A = 3.4

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Example Question #83 : Functions And Lines

$\left \lceil x \right \rceil$ is defined as the least integer greater than or equal to .

Define $f(x) = \left \lceil x^{2} + x + 2 \right\rceil$ .

Evaluate f(5.5) .

Possible Answers:

f(5.5) = 37

f(5.5) = 32

f(5.5) = 35

f(5.5) = 38

f(5.5) = 33

Correct answer:

f(5.5) = 38

Explanation:

$f(x) = \left \lceil x^{2} + x + 2 \right\rceil$

Plug in 5.5:

$f(5.5) = \left \lceil 5.5^{2} + 5.5 + 2 \right\rceil$

$f(5.5) = \left \lceil 30.25 + 5.5 + 2 \right\rceil$

$f(5.5) = \left \lceil 37.75 \right\rceil = 38$

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Example Question #3361 : Algebra 1

$f\left ( x \right ) = \sqrt{x}$

$g\left ( x \right ) = 2x-3$

$h\left ( x \right ) = x^{2}$

Find $f\left ( g\left ( h\left ( x \right ) \right ) \right )$ .

Possible Answers:

$2x^{2}-3$

$\sqrt{x^{3}}$

2x-3

$\sqrt{2x^{2}-3}$

Correct answer:

$\sqrt{2x^{2}-3}$

Explanation:

Plug h(x) into g(x) .

$g\left ( x \right ) =2x-3$

$g\left ( h\left ( x \right ) \right ) = 2\times h(x) - 3 = 2x^{2} - 3$

Now plug that into f(x) :

$f\left ( g\left ( h\left ( x \right ) \right ) \right )= \sqrt{g(h(x))} = \sqrt{2x^{2}-3}$

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Example Question #32 : Solving Equations

Solve for f(x) . When x=2 .

f(x)=5x^3+2x-24

Possible Answers:

f(x)=20

f(x)=10

f(x)=-15

f(x)=14

f(x)=-20

Correct answer:

f(x)=20

Explanation:

Given the equation,

f(x)=5x^3+2x-24 and x=2

Plug in for to the equation, f(2)=5(2)^3+2(2)-24

Solve and simplify.

f(2)=5(8)+4-24

f(2)=40+4-24

f(2)=44-24

f(2)=20

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Example Question #33 : Solving Equations

$f(x)=\frac{4x-2}{x+3}, x\neq-3$

Solve for f(x) , when x=0 .

Possible Answers:

$f(x)=\frac{1}{3}$

f(x)=0

$f(x)=\frac{-1}{3}$

$f(x)=\frac{-2}{3}$

$f(x)=\frac{2}{3}$

Correct answer:

$f(x)=\frac{-2}{3}$

Explanation:

$f(x)=\frac{4x-2}{x+3}, x\neq-3$

Plug in the value for .

$f(0)=\frac{4(0)-2}{(0)+3}$

Simplify

$f(0)=\frac{0-2}{3}$

Subtract

$f(0)=\frac{-2}{3}$

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Example Question #31 : Algebraic Functions

For the following equation, if x = 2, what is y?

y=x^3-4x+9

Possible Answers:

Correct answer:

Explanation:

On the equation, replace x with 2 and then simplify.

y=x^3-4x+9

y=(2)^3-4(2)+9

y=8-8+9

y=9

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Example Question #32 : Algebraic Functions

Solve for f(3) when $f(x)= \frac{x^{2}+12x}{3x}$ .

Possible Answers:

f(3)=3

f(3)=5

f(3)=16

Does not exist

f(3)=9

Correct answer:

f(3)=5

Explanation:

Plug 3 in for x:

$f(3)=\frac{(3^{2})+12*3}{3*3}$

Simplify:

= $\frac{9+36}{9}$

= 5

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Example Question #11 : Function Notation

What is f(7) of the following equation?

$f(x)=x^{2}+15x+35$

Possible Answers:

189

188

187

190

Correct answer:

189

Explanation:

To complete an equation with a function, plug the number inside the parentheses into the equation for and solve algebraically.

In this case the $f(7)=7^{2}+(15*7)+35$

Square the 7 and multiply to get f(7)=49+105+35

Add the numbers to get the answer f(7)=189 .

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Example Question #141 : Functions And Graphs

$\textup{If }f(p)= p^{3}-3p,\;\textup{what is the value of }f(5)\textup{?}$

Possible Answers:

107

110

140

Correct answer:

110

Explanation:

$\textup{Just plug in 5 every time you see }p\textup{ in the equation and solve:}$

$\left ( 5\right )^{3}-3\left ( 5\right )=125-15=110$

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Functions And Lines

Example Question #81 : Functions And Lines

Example Question #83 : Functions And Lines

Example Question #3361 : Algebra 1

Example Question #32 : Solving Equations

Example Question #33 : Solving Equations

Example Question #31 : Algebraic Functions

Example Question #32 : Algebraic Functions

Example Question #11 : Function Notation

Example Question #141 : Functions And Graphs

All Algebra 1 Resources

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