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Algebra II : Function Notation

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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 #42 : Function Notation

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

Possible Answers:

$\frac{1}{15}$

$-\frac{11}{6}$

$-\frac{1}{15}$

$-\frac{6}{5}$

$-\frac{11}{15}$

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 #43 : Function Notation

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 #44 : 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 #46 : Function Notation

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

Possible Answers:

$\frac{47}{6}$

$\frac{97}{6}$

$\frac{81}{4}$

$\frac{107}{15}$

$\frac{56}{3}$

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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Example Question #41 : Function Notation

Which of the following is the equation of a vertical asymptote of the graph of the function $f(x) = \frac{x+7}{x^{2}- 16}$ ?

(a) x= -7

(b) x= -4

Possible Answers:

(a) only

(b) and (c) only

All three of (a), (b), and (c)

(b) only

Correct answer:

(b) and (c) only

Explanation:

The vertical asymptote(s) of the graph of a rational function such as f(x) can be found by evaluating the zeroes of the denominator after the rational expression is reduced. The expression is in simplest form, so set the denominator equal to 0 and solve for :

$x^{2} - 16 = 0$

Add 16 to both sides:

$x^{2} - 16 + 16 = 0+ 16$

$x^{2} =16$

Take the positive and negative square roots:

$x = -\sqrt{16 } = -4$

$x = \sqrt{16 } = 4$

The graph of f(x) has two vertical asymptotes, the graphs of the lines x = -4 and x= 4 .

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Example Question #49 : Function Notation

If g(x)=5x+6x^2+3 and f(x)=x-4 what is g(f(x)) ?

Possible Answers:

6x^2-53x+119

6x^2+5x-1

6x^2+5x+79

6x^2-43x+79

Correct answer:

6x^2-43x+79

Explanation:

g(f(x)) is a composite function which means that the inside function is plugged into the outside function. So in this case, f(x) is plugged into g(x) . In other words, replace the f(x) expression each time there is an in the g(x) expression.

In this case x-4 would be plugged into each in the g(x) expression. See below:

5(x-4)+6(x-4)^2+3

This is then simplified to:

5x-20+6x^2-48x+96+3

And then further simplified to:

6x^2-43x+79

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Algebra II : Function Notation

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Function Notation

Example Question #42 : Function Notation

Example Question #43 : Function Notation

Example Question #44 : Function Notation

Example Question #45 : Function Notation

Example Question #46 : Function Notation

Example Question #47 : Function Notation

Example Question #41 : Function Notation

Example Question #49 : Function Notation

All Algebra II Resources

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