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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #38 : Function Notation

Determine $f(\frac{1}{3})$ if $f(x)= \frac{1}{2x}$ .

Possible Answers:

$\frac{3}{2}$

$\frac{3}{7}$

$\frac{1}{6}$

$\frac{7}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

To determine the output of f(x) , substitute the value of $\frac{1}{3}$ as a replacement of .

$f(\frac{1}{3})= \frac{1}{2(\frac{1}{3})} = \frac{1}{\frac{2}{3}}$

Rewrite the complex fraction using a division sign.

$1\div \frac{2}{3}$

Take the reciprocal of the second term and change the division sign to a multiplication sign.

$1\div \frac{2}{3} = 1\times \frac{3}{2}$

The answer is: $\frac{3}{2}$

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Example Question #39 : Function Notation

Determine f(g(3)) if f(x) = 3 and g(x)=3x .

Possible Answers:

Correct answer:

Explanation:

Substitute three into the function of g(x)=3x to solve for g(3) .

g(3)=3(3)=9

Substitute this value into the function f(x) = 3 .

f(9)=3

There is no x-variable to substitute nine, which means the function is equal to three.

The answer is:

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Example Question #40 : Function Notation

If x=4 and y=6 , determine: 2(x+2y)

Possible Answers:

Correct answer:

Explanation:

Substitute the assigned values into the expression.

2(x+2y)=2(4+2(6))

Simplify the inside parentheses.

= 2(4+12) = 2(16) = 32

The answer is:

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Example Question #41 : Function Notation

What is the value of 3b^2-5c^3 if b=2 and c=-1 ?

Possible Answers:

Correct answer:

Explanation:

Substitute the assigned values into the expression.

3b^2-5c^3 = 3(2)^2-5(-1)^3

Simplify by order of operations.

= 3(4)-5(-1) = 12+5 = 17

The answer is:

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Example Question #171 : Functions And Graphs

Determine the value of $\frac{a}{c}-\frac{b}{d}$ if: a=1, b=2,c=3, d=5 .

Possible Answers:

$-\frac{11}{15}$

$-\frac{6}{5}$

$-\frac{11}{6}$

$\frac{1}{15}$

$-\frac{1}{15}$

Correct answer:

$-\frac{1}{15}$

Explanation:

Substitute the values of a=1, b=2,c=3, d=5 into the expression.

$\frac{a}{c}-\frac{b}{d} = \frac{1}{3}-\frac{2}{5}$

In order to subtract these fractions, we will need a least common denominator.

Multiply the denominators together for the LCD. Convert the two fractions.

$\frac{1}{3}-\frac{2}{5} = \frac{1(5)}{3(5)}-\frac{2(3)}{5(3)} = \frac{5}{15}-\frac{6}{15}$

Subtract the numerators now that the denominators are common.

The answer is: $-\frac{1}{15}$

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Example Question #172 : Functions And Graphs

Determine the value of a^3-b^2-c if: a=-1, b=-3, c=-5

Possible Answers:

Correct answer:

Explanation:

Given the expression a^3-b^2-c and the assigned values, substitute the values into the expression.

(-1)^3-(-3)^2-(-5)

Simplify this expression by order of operations.

-1-(9)+5 = -10+5 = -5

The answer is:

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Example Question #41 : Function Notation

Evaluate a^2-b^3 if a=-6 and b =-3

Possible Answers:

Correct answer:

Explanation:

Substitute the known values into the expression.

a^2-b^3 = (-6)^2-(-3)^3

Simplify the expression.

36-(-27) = 36+27 = 63

The answer is:

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Example Question #45 : Function Notation

If a=-1 and b= -2 , what is $a^b\times b^a$

Possible Answers:

$-\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{2}$

Explanation:

Substitute the assigned values into the expression.

$(-1)^{(-2)}\times (-2)^{(-1)}$

Simplify the negative exponents by rewriting both terms as fractions.

$x^{-a} =\frac{1}{x^a}$

$(-1)^{(-2)}\times (-2)^{(-1)}= \frac{1}{(-1)^2} \times \frac{1}{(-2)^{1}}$

Simplify the fractions.

$1\times \frac{1}{-2} = -\frac{1}{2}$

The answer is: $-\frac{1}{2}$

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Example Question #173 : Functions And Graphs

If f(2)=5 , what must be? y = 3x(A-7)

Possible Answers:

$\frac{56}{3}$

$\frac{107}{15}$

$\frac{81}{4}$

$\frac{97}{6}$

$\frac{47}{6}$

Correct answer:

$\frac{47}{6}$

Explanation:

Substitute the known value of x=2, y=5 into the equation.

5= 3[2](A-7)

Simplify the equation.

5=6(A-7)

Solve the right side by distribution.

5=6A-42

Add 42 on both sides.

5+42=6A-42+42

47=6A

Divide by six on both sides.

$\frac{47}{6}=\frac{6A}{6}$

The answer is: $\frac{47}{6}$

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Example Question #47 : Function Notation

If f(2) = 4 , what must equal in f(x) = 5x-k ?

Possible Answers:

Correct answer:

Explanation:

The term f(2) = 4 means that f(x)=4 when x=2 .

Substitute the terms in the function to solve for .

4 = 5(2)-k

Solve for .

4 = 10-k

Subtract 10 on both sides.

4 -10= 10-k-10

-6 =-k

Divide by negative one to eliminate the negative signs.

$\frac{-6 }{-1}=\frac{-k}{-1}$

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #38 : Function Notation

Example Question #39 : Function Notation

Example Question #40 : Function Notation

Example Question #41 : Function Notation

Example Question #171 : Functions And Graphs

Example Question #172 : Functions And Graphs

Example Question #41 : Function Notation

Example Question #45 : Function Notation

Example Question #173 : Functions And Graphs

Example Question #47 : Function Notation

All Algebra II Resources

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