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Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #43 : Inverse Functions

Determine the inverse of: y=-3x-20

Possible Answers:

$y=-\frac{1}{3}x+\frac{20}{3}$

$y=3x+\frac{10}{3}$

$y=-\frac{1}{3}x-\frac{20}{3}$

$y=-\frac{1}{3}x+\frac{10}{3}$

$y=\frac{1}{3}x-\frac{20}{3}$

Correct answer:

$y=-\frac{1}{3}x-\frac{20}{3}$

Explanation:

Interchange the x and y-variable.

x=-3y-20

Add twenty on both sides.

x+20=-3y-20+20

x+20=-3y

Divide both sides by negative three.

$\frac{x+20}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is: $y=-\frac{1}{3}x-\frac{20}{3}$

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Example Question #44 : Inverse Functions

Determine the inverse of y=-9x-5

Possible Answers:

$y= -9x+\frac{5}{9}$

$y= -\frac{1}{9}x+\frac{5}{9}$

$y= -\frac{1}{9}x-\frac{9}{5}$

$y= 9x+\frac{5}{9}$

$y= -\frac{1}{9}x-\frac{5}{9}$

Correct answer:

$y= -\frac{1}{9}x-\frac{5}{9}$

Explanation:

Interchange the x and y-values.

x=-9y-5

Solve for y. Add five on both sides.

x+(5)=-9y-5+(5)

The equation becomes: x+5 =-9y

Divide by negative nine on both sides.

$\frac{x+5}{-9} =\frac{-9y}{-9}$

The answer is: $y= -\frac{1}{9}x-\frac{5}{9}$

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Example Question #45 : Inverse Functions

Determine the inverse: y=3(x-10)

Possible Answers:

$y=-\frac{1}{3}x-10$

$y=\frac{1}{3}x+30$

$y=\frac{1}{3}x+10$

$y=\frac{1}{3}x-10$

$y=-\frac{1}{3}x+30$

Correct answer:

$y=\frac{1}{3}x+10$

Explanation:

Interchange both the x and y- variables.

x=3(y-10)

Solve for y. Distribute the three through both terms of the binomial.

x=3y-30

Add 30 on both sides.

x+30=3y-30+30

x+30=3y

Divide by three on both sides.

$\frac{x+30}{3}=\frac{3y}{3}$

Simplify both sides.

The answer is: $y=\frac{1}{3}x+10$

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Example Question #46 : Inverse Functions

Determine the inverse function: y=9x+26

Possible Answers:

$y=\frac{1}{9}x-3$

$y=\frac{1}{9}x-\frac{26}{9}$

$y=\frac{1}{9}x-\frac{1}{3}$

$y=-\frac{1}{9}x+\frac{26}{9}$

$y=-9x-\frac{26}{9}$

Correct answer:

$y=\frac{1}{9}x-\frac{26}{9}$

Explanation:

Interchange the x and y-variables.

x=9y+26

Solve for y. Subtract 26 from both sides.

x-26=9y+26-26

The equation becomes:

x-26=9y

Divide by nine on both sides.

$\frac{x-26}{9}=\frac{9y}{9}$

Simplify both fractions.

The answer is: $y=\frac{1}{9}x-\frac{26}{9}$

Report an Error

Example Question #41 : Inverse Functions

Determine the inverse of: y= 7x-4

Possible Answers:

$y=\frac{1}{7}x-\frac{4}{7}$

$y=\frac{4}{7}x-\frac{4}{7}$

$y=\frac{1}{7}x+\frac{4}{7}$

$y=-7x+\frac{4}{7}$

y=-7x+4

Correct answer:

$y=\frac{1}{7}x+\frac{4}{7}$

Explanation:

Interchange the x and y variables and solve for y.

x= 7y-4

Add four on both sides.

x+4= 7y-4+4

Simplify both sides.

x+4= 7y

Divide by seven on both sides.

$\frac{x+4}{7}= \frac{7y}{7}$

The answer is: $y=\frac{1}{7}x+\frac{4}{7}$

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Example Question #48 : Inverse Functions

Determine the inverse of: y=-(x+6)

Possible Answers:

y=-6x

y=-x-6

y=x-6

y=-x+6

y=x+6

Correct answer:

y=-x-6

Explanation:

In order to determine the inverse, interchange the x and y-variables.

x=-(y+6)

Divide by negative one on both sides.

$\frac{x}{-1}=\frac{-(y+6)}{-1}$

Simplify both sides.

-x = y+6

Subtract six from both sides.

-x-6 = y+6-6

The answer is: y=-x-6

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Example Question #49 : Inverse Functions

Determine the inverse of: y= 2x-50

Possible Answers:

$y=\frac{1}{2}x-25$

$y=\frac{1}{2}x+25$

$y=-\frac{1}{2}x-50$

$y=-\frac{1}{2}x-25$

y=-2x-50

Correct answer:

$y=\frac{1}{2}x+25$

Explanation:

Interchange the x and y-variables.

x= 2y-50

Add 50 on both sides.

x+50= 2y-50+50

The equation becomes:

x+50= 2y

Divide both sides by two and split the fraction.

$\frac{x+50}{2}=\frac{ 2y}{2}$

The answer is: $y=\frac{1}{2}x+25$

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Example Question #42 : Inverse Functions

Determine the inverse: y=-4x-19

Possible Answers:

$\frac{1}{4}x-\frac{4}{19}$

$-\frac{1}{4}x+\frac{19}{4}$

$-\frac{1}{4}x-19$

$4x-\frac{19}{4}$

$-\frac{1}{4}x-\frac{19}{4}$

Correct answer:

$-\frac{1}{4}x-\frac{19}{4}$

Explanation:

Interchange the x and y-variables.

x=-4y-19

Add 19 on both sides.

x+19=-4y-19+19

x+19=-4y

Divide by negative four on both sides.

$\frac{x+19}{-4}=\frac{-4y}{-4}$

Simplify both sides.

The answer is: $-\frac{1}{4}x-\frac{19}{4}$

Report an Error

Example Question #51 : Inverse Functions

Determine $f^{-1}(x)$ if f(x)= 4x-80 .

Possible Answers:

$\frac{1}{4}x-20$

$\frac{1}{20}x-20$

$\frac{1}{20}x-\frac{1}{20}$

$\frac{1}{4}x+20$

$-\frac{1}{4}x-20$

Correct answer:

$\frac{1}{4}x+20$

Explanation:

Replace the f(x) term with the y-variable.

y= 4x-80

Interchange the x and y-variables.

x= 4y-80

Add 80 on both sides.

x+80= 4y-80+80

x+80= 4y

Divide by four on both sides.

$\frac{x+80}{4}= \frac{4y}{4}$

Simplify both sides.

$f^{-1}(x)=y=\frac{1}{4}x+\frac{80}{4}$

The answer is: $\frac{1}{4}x+20$

Report an Error

Example Question #771 : Algebra Ii

Determine the inverse function of y=-3x+24

Possible Answers:

$y=-3x -\frac{8}{3}$

$y=-\frac{1}{3}x +8$

y=-3x -8

$y=-\frac{1}{3}x +\frac{8}{3}$

$y=-\frac{1}{3}x -8$

Correct answer:

$y=-\frac{1}{3}x +8$

Explanation:

Interchange the x and y-variables.

x=-3y+24

Subtract 24 from both sides.

x-24=-3y+24-24

The equation becomes:

x-24=-3y

Divide by negative three on both sides.

$\frac{x-24}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is: $y=-\frac{1}{3}x +8$

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Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #43 : Inverse Functions

Example Question #44 : Inverse Functions

Example Question #45 : Inverse Functions

Example Question #46 : Inverse Functions

Example Question #41 : Inverse Functions

Example Question #48 : Inverse Functions

Example Question #49 : Inverse Functions

Example Question #42 : Inverse Functions

Example Question #51 : Inverse Functions

Example Question #771 : Algebra Ii

All Algebra II Resources

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