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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #23 : Algebraic Functions

Given $g\left ( x \right ) = 2x-5$

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

Possible Answers:

2x-5

4x-15

$4x^{2} -25$

$\left (2x-5 \right )^{2}$

$4x^{}2 + 25$

Correct answer:

4x-15

Explanation:

$g\left ( x \right ) = 2x-5$

Substituting g(x) in place of above equation one gets the following:

$2\left ( 2x-5 \right ) - 5$

which, after simplification, gives us the correct answer which is

4x-15

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Example Question #24 : Algebraic Functions

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

and $g\left ( x \right ) = 2x+3$

Find $f\left ( -2 \right ) - g\left ( -2 \right )$

Possible Answers:

Correct answer:

Explanation:

$f\left ( -2 \right ) - g\left ( -2 \right ) = \left [-\left ( -2 \right )^{2} - 3 \right ] - \left [ 2\left ( -2 \right ) +3\right ]$

=-4-3-(-4+3)

=-7-(-1)

=-7+1

=-6

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Example Question #122 : Basic Statistics

There exists a function f(x) = 3x + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?

Possible Answers:

Correct answer:

Explanation:

First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:

average = (8 + 11 + 14 + 17 + 20) / 5 = 14

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Example Question #25 : Algebraic Functions

Solve the function for . When f(x)=16

What does equal when, f(x)=16

$f(x)=x^{2}-9$

Possible Answers:

$\pm5$

-5

$\sqrt{5}$

Correct answer:

$\pm5$

Explanation:

Plug 16 in for f(x) . 16=x^2-9

Add 9 to both sides. x^2=25

Take the square root of both sides. $\sqrt{25}$ = $\sqrt{x^{2}}$

Final answer is $\pm5$

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Example Question #31 : How To Find F(X)

Define $f (x) = 3 - \sqrt{x-1}$ and $g\left ( x\right ) = 3 + \sqrt{x-1}$ .

Evaluate $\left (f-g \right ) (17)$ .

Possible Answers:

$\left (f-g \right ) (17)$ is undefined.

Correct answer:

Explanation:

First evaluate f (17) and g(17) , then subtract.

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

$f (17) = 3 - \sqrt{17-1} = 3 - \sqrt{16} = 3-4 = -1$

$g\left ( x\right ) = 3 + \sqrt{x-1}$

$g(17) = 3 + \sqrt{17-1} = 3 + \sqrt{16} = 3+4 = 7$

$\left (f-g \right ) (17) = f(17)-g(17) = -1-7 = -8$

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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 + 5

t^2 - 4t + 1

t^2 + 4t + 1

2t^2 + 4t + 17

2t^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 #82 : Functions And Lines

Define g (x) = 5x +7 .

If g (A) = 24 , evaluate .

Possible Answers:

A = 3.4

A=127

A = 11.8

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) = 38

f(5.5) = 32

f(5.5) = 35

f(5.5) = 33

f(5.5) = 37

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 #84 : Functions And Lines

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

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

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

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

Possible Answers:

2x-3

$\sqrt{x^{3}}$

$2x^{2}-3$

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

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)=14

f(x)=10

f(x)=-15

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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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #23 : Algebraic Functions

Example Question #24 : Algebraic Functions

Example Question #122 : Basic Statistics

Example Question #25 : Algebraic Functions

Example Question #31 : How To Find F(X)

Example Question #81 : Functions And Lines

Example Question #82 : Functions And Lines

Example Question #83 : Functions And Lines

Example Question #84 : Functions And Lines

Example Question #32 : Solving Equations

All Algebra 1 Resources

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