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SAT Math : Algebra

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Example Questions

Example Question #142 : Algebraic Functions

$f(x) = \left | 15-x^{2}\right |$ If f(x) = 10 , what is the positive value of that satisfies the equation?

Possible Answers:

Correct answer:

Explanation:

Since the final answer is with the absolute value, then $15-x^{2}$ can be or . To get , you have to plug in $\sqrt{5}$ for $(15-\sqrt[2]{5}=10)$ . To get , you plug in $(15-5^{2}=10)$ .

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Example Question #143 : Algebraic Functions

Find f(x) : $3x-\frac{6}{f(x)}=8$

Possible Answers:

$f(x)=\frac{6}{8-3x}$

$f(x)=\frac{6}{3x-8}$

$f(x)= \frac{1}{3}x+\frac{4}{3}$

$f(x) = -\frac{1}{2}x+4$

$f(x) = \frac{1}{2}x+4$

Correct answer:

$f(x)=\frac{6}{3x-8}$

Explanation:

To simplify this equation, first subtract on both sides of the equation.

$-\frac{6}{f(x)}=8-3x$

Multiply f(x) on both sides of the equation to eliminate the denominator on the left side of the equation.

$-\frac{6}{f(x)}=8-3x$

-6=f(x)(8-3x)

Divide by (8-3x) on both sides of the equation to isolate f(x) .

$\frac{-6}{(8-3x)}=f(x)$

The negative sign can be extracted out in front of the fraction.

$f(x)=-\frac{6}{8-3x}$

The negative sign can then be distributed with the denominator.

$f(x)=\frac{6}{-(8-3x)} = \frac{6}{3x-8}$

The correct answer is: $f(x)=\frac{6}{3x-8}$

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Example Question #32 : Algebraic Functions

For which value of are the following two functions equal?

$F(x)=2x+3^x+\frac{9x}{3}$

$G(x)=\frac{2^x+4^x}{2}-4x-5x+1$

Possible Answers:

Correct answer:

Explanation:

It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).

Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

The correct answer is 4 because

F(x) = 2x + 3^x+ (9x/3) = 2(4) + 3⁴ + ((9 * 4)/3) = 101, and

G(x) = (((2⁴ + 4⁴)/2) - 4 * 4) – 5(4) + 1 = 101.

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Example Question #101 : How To Find F(X)

Define f(x) = | 3x - 9| + 8 .

Which of the following is an alternative way of defining ?

Possible Answers:

$f(x) = \left\{\begin{matrix}3x -17 & x \ge 3 \\ -3x+17 & x < 3 \end{matrix}\right.$

$f(x) = \left\{\begin{matrix}-3x+17 & x \ge 3 \\3x -1 & x < 3 \end{matrix}\right.$

$f(x) = \left\{\begin{matrix}3x -1 & x \ge 3 \\ -3x+17 & x < 3 \end{matrix}\right.$

$f(x) = \left\{\begin{matrix} 3x+17 & x \ge 3 \\ - 3x -1 & x < 3 \end{matrix}\right.$

$f(x) = \left\{\begin{matrix}3x -1 & x \ge 3 \\ -3x+1 & x < 3 \end{matrix}\right.$

Correct answer:

$f(x) = \left\{\begin{matrix}3x -1 & x \ge 3 \\ -3x+17 & x < 3 \end{matrix}\right.$

Explanation:

If the expression between the absolute value bars is nonnegative, then | 3x - 9| = 3x-9 , and

f(x) = | 3x - 9| + 8

= 3x - 9 + 8

= 3x -1

This happens if:

$3x - 9 \ge 0$

$3x - 9+ 9 \ge 0 + 9$

$3x \ge 9$

$3x \div 3 \ge 9 \div 3$

$x \ge 3$

If the expression between the absolute value bars is negative, then | 3x - 9| = - (3x-9) = -3x+9 , and

f(x) = | 3x - 9| + 8

= -3x+9 + 8

= -3x+17

This happens if:

3x - 9 < 0 , or

x <3

Therefore, the function can be restated as

$f(x) = \left\{\begin{matrix}3x -1 & x \ge 3 \\ -3x+17 & x < 3 \end{matrix}\right.$ .

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Example Question #1074 : Algebra

f(x)=3x^2 -12x and f(3t)=36 .

If is a positive integer, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

f(x)=3x^2 -12x

f(3t)=36

First, substitute 3t for x and set the equation equal to 36

3(3t)^2 -12(3t)=36

3(9t^2) -36t=36

Then manipulate the equation so the equation equals 0.

27t^2 -36t-36=0

Factor out 9.

9(3t^2 -4t-4)=0

Divide by 9

$\frac{9(3t^2 -4t-4)}{9}=\frac{0}{9}$

3t^2 -4t-4=0

Factor the equation and solve

(3t+2)(t-2)=0

$t-2=0\: and\: 3t+2=0$

$t=2\: and\: t=-\frac{2}{3}$

Because t is a positive integer, the answer is t=2.

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Example Question #1075 : Algebra

If f(x)=2x+4 , what is the value of f(2) ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=2x+4

f(2)=2(2)+4

f(2)=4+4

f(2)=8

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Example Question #1071 : Algebra

If f(x)=6x-12 , what is -2f(3)+2 ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=6x-12

-2f(3)+2=-2(6(3)-12)+2

=-2(18-12)+2

=-2*6+2

=-12+2

=-10

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Example Question #142 : Algebraic Functions

If f(x)=x^2-3 , then what is 4f(x)+1 for all real values of ?

Possible Answers:

4x^2+1

4x^2+3

4x^2-11

4x^2-2

4x^2-12

Correct answer:

4x^2-11

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=x^2-3

4f(x)+1=4(x^2-3)+1

=4x^2-12+1

=4x^2-11

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Example Question #141 : Algebraic Functions

If f(x)=x^2+2 , then what is f(x+1) for all real values of ?

Possible Answers:

x^2+3

x+3

x^2+3x

x^2+2x+3

x^2+2x+1

Correct answer:

x^2+2x+3

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=x^2+2

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

=x^2+x+x+1+2

=x^2+2x+3

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Example Question #151 : Algebraic Functions

If f(x)=-x^2+x , then what is f(x+2) for all real values of ?

Possible Answers:

-x^2+2

x^2+5x+6

-x^2-3x-2

-x^2-4x+4

-x^2-3x+2

Correct answer:

-x^2-3x-2

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=-x^2+x

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

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

=-x^2-4x-4+x+2

=-x^2-3x-2

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #142 : Algebraic Functions

Example Question #143 : Algebraic Functions

Example Question #32 : Algebraic Functions

Example Question #101 : How To Find F(X)

Example Question #1074 : Algebra

Example Question #1075 : Algebra

Example Question #1071 : Algebra

Example Question #142 : Algebraic Functions

Example Question #141 : Algebraic Functions

Example Question #151 : Algebraic Functions

All SAT Math Resources

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