Unit 1 Review

Absolute Value Equations and Inequalities

100

Solve for all values of x in simplest form. 

5 + 2 |2x + 4| = 9

x = -1

x = -3

200

Solve for all values of xx in simplest form.

−3|8−x|−5=−11

x = 6 & x = 10

300

Solve the following inequality algebraically. 

|x + 3| <= 9

-12<= x <= 6

400

Solve the following inequality algebraically. 

|x - 3| >= 11

x<= -8 OR x>= 14

500

Solve the following inequality algebraically. 

2|x - 5| + 7 < 11

3 < x < 7

Inverses

100

For the function f(x) = 9x + 4, find f^-1(x). 

f^-1(x) = (x-4) / 9

200

Graph the function f(x) = x² - 6x + 12. 

Is the function one-to-one, not a function, or function but not one-to-one?

Function, but not one-to-one. 

300

For the function f(x) = (5x)^1/3, find f^-1(x). 

f^-1(x) = (x³)/5

400

Find the inverse function of the function f(x)=(5x)^-5/9 on the domain x > 0.

f⁻¹(x) = (x^-9/5) / 5

500

Find the inverse function of the function f(x) = 4x^5/7 on the domain x ≥ 0.

f⁻¹(x)=(x/4)^5/7

Transformations

100

Take the parent function y = x²

Translate it 5 units to the right and 5 units down. 

What is the function now?

y = (x - 5)² - 5

200

Take the function y = |x|. 

Translate it 1 unit to the right, and reflect it over the x-axis. 

y = - |x - 1|

300

Take the function y = x², translate it 4 units up, 1 unit to the left, and reflect it across the x axis. 

y = - (x + 1)² + 4

400

Take the function, y = sqrt(x) and translate it 3 units to the right, and 3 units down. 

y = sqrt(x - 3) - 3

500

Take the function y = 2^x. translate it 2 units to the left, and reflect it over the x-axis. 

y = -2^{x + 2}

Piecewise

100

f(x)={x+2 for x =/ 0 

        {4    for x=0

Find f(0)

f(0) = 4

200

f(x)={(x+6)²+2 for x≤−5

       { −6x+19 for x≥3

Find f(1)

f(1) = undefined

300

f(x)={(x−5)2−3 for x =/ 3

        {4             for x = 3

Find f(6)

Final Answer: -1

400

f(x)= {−(x+6)²+1     for x<−3

         {−5                 for x=−3

         {2x                  for −3<x≤2

Find f(−1)

f(-1) = -2

500

f(x)={−(x−3)²+8 for 0<x<3

        {3 for x=3

        {−x+7  for 3<x<6

Find f(1)

f(1) = 4

Systems of Inequalities

100

Which point would be a solution to the system of linear inequalities shown below?

y>4x−5       y≥(3/5)x−1

a) (5,7)    b) (-5,4)

c) (10,-7) d) (0,-6)

Correct answer: (-5,4)

200

Which point would be a solution to the system of linear inequalities shown below?

y>−2x+2            y>(1/2)x+2

a) (2,7)       b) (-6,10)

c) (-12,9)    d) (6,-10)

Correct answer: (2,7)

300

Which point would not be a solution to the system of linear inequalities shown below?

y≥−(1/3)x+8        y ≤ 2x + 1

Correct Answer: (3,3)

3≥−(1/3)(3)+8                  3≤2(3)+1

     3≥7                                   3≤7

FALSE                                    TRUE

At least one is UNTRUE, so (3,3) is NOT a solution.

(Which makes it the answer to this question.)

400

Which point would be a solution to the system of linear inequalities shown below?

y≤−(2/3)x−2        y≥−(1/2)x−1

a) (6,-5)      b) (0,-1)

c) (-6,-7)     d) (-12,5)

Correct Answer: (-12,5)

500

y>−(3/2)x+3          y<(3/4)x−1

What point would satisfy BOTH inequalities?

a) (-4,3)      b) (0,5)

c) (10,1)      d) (-5,-6)

Correct Answer: (10,1)