Linear Functions

1.Given f(x) = -3/4 x -2

a.What is the slope and y - intercept

Slope = ------------------------

y - intercept co-ordinate ---------------------

b.What is the average rate of change?

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c.Is the function increasing or decreasing?

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Quadratic Functions

2.Given the quadratic function

f(x) = -3 x² + 6x + 2

a.Which way does the parabola (cup) open? Up or Down

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b.What are the co-ordinates of its vertex?

(h, k) --------------------------------------------

c.What is the equation of the axis of symmetry?

x =

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d.What is its y-intercept?

y- intercept co-ordinate -------------------------------

3.Given the function f (x) = 2x² -4 x -5

a.Does it have a maximum or a minimum?

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b.What x value does the maximum or minimum occur at?

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c.What is the maximum or minimum value?

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Solving Inequalities Involving Quadratic Functions

4.Given f(x) = (-x + 1) (x+3) = - x² - 2x + 3 > 0

Solve for x

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5.Given f(x) = (2x + 3) (3x - 2) = 6 x ² + 5x - 6 > 0

Solve for x

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Polynomial Properties

6.Given

f (x) = (x+1) ² (x -1)

a.Identify the degree of the polynomial

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b.What is the maximum number of turning points?

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c.Identify the real zeros and their multiplicities

Real Zero Multiplicity

x=

x =

d.At each zero does the graph touch or cross the x-axis

Real Zero Cross or Touch x-Axis

x=

x =

e.What is the value of the y-intercept?

Answer----------------------------

Polynomial and Rational Function Inequality

7.Solve f (x) = (x-7)³ >0

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Composite Functions

8.Given f(x) = 2/x

g(x) = 2x² + 3

Find

a.(f o g) (2)

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b.(g o f) (1)

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Inverse Functions

9.Given f: {(1,5), (a, b), (7,3), (8,9)}

Find f ^-1

f^-1: {}

10.Given f(x) = 4x + 7

Find f ^-1 (x)

Exponential Functions

11.Solve for x

(1/ 9) ^{x - 2} = 9 ^x

x = -------------------------

12.3 ^{x+ 1} = 27 ^2x

x = ---------------------------------

Hint: 27 = 3 ³

Logarithmic Functions

13.Change exponential to logarithmic form

5.7 ^x = 22.8

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14.Change logarithmic statement to exponential statement

log ₇ 5.4 = w

15.Determine

a.log 151.2 -----------------------

b.ln (1.31) -------------------------

c.log ₆ (102.3)

16.Solve for x

10 ^{2x + 1} = 110

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Hint: Change to logarithmic form

log ₁₀ (#) = log (#) on calculator

Logarithmic Application

17.The hydrogen ion concentration of mouthwash is 10 ^-6 per mole liter. What is its pH?

pH ----------------------

18.The sound intensity of a dishwasher is 10 ^-9 watts per meter square. How high is this sound level in dB?

dB -----------------------

Extra Credit

19.If log (2a + b) = -2

and log ₅ (a + 2b) = 3

What is a and b?

a = -------------------------b = ----------------------------------------

Hint: Convert a and b to exponentials and solve the resulting equation for a and b