Mat 171 - Ch. 2/3 Review

Functions

100

Find f(5):

x²+5x-4

46

200

State the domain:

(x²+5x+4) / (x + 1)

(-infinity , -1) U (-1, infinity)

or

all x except -1

300

Find the net change of f(x)=x²-4x+1 on [1, 5].

8

400

Suppose f(x)=ax+b, f(2)=7, and f(-3)=-8.  

Find f(10).

31

500

Find the difference quotient:

x²-4x+1

2x+h-4

Transformations

100

Write the equation y=x² shifted left 4 units.

y=(x+4)²

200

If f(x)=|x|, write a function g(x) that is shifted right 3, reflected across the x-axis, and shifted down 2.

g(x)=-|x-3|-2

300

Describe the transformation:

y=-3(x-2)²+5

Right 2

Vertical stretch of 3, reflected over the x-axis

Up 5

400

If f has D: [-4, 6] and R: [-2, 8], give the domain and range of:

g(x)=f(x-3)+5

D: [-1, 9]

R: [3, 13]

500

The graph of f is shifted left 2, shrunk horizontally by 1/3, reflected over the x-axis, and shifted down 5.  Write g in terms of f.

g(x)=-f(3x+6)-5

or

g(x)=-f(3(x+2))-5

Quadratics

100

Solve the following:

x²-x-6=0

x=3, -2

200

Solve the following:

2x²+72=0

x=6i, -6i

300

A quadratic function has f(-1)=6, f(1)=2, and f(3)=6.  Find its vertex.

(1, 2)

400

Solve:

x²-3x+9=0

x=3/2+(3sqrt(3))/2 i

x=3/2-(3sqrt(3))/2 i

500

Complete the square to write the equation in vertex form:

f(x)=x²-4x+1

f(x)=(x-2)^2-3

Polynomials

100

Factor completely: x³-4x

x(x-2)(x+2)

200

Find the remainder when P(x)=2x³-5x²+x+7 is divided by x-2.

5

300

Divide (x⁴-3x³+x-2)/(x²-5x+1).

x²+2x+9+(44x-11)/(x²-5x+1)

400

Find a polynomial with zeros: -2, 1, 4, where 1 has a multiplicity of 2.

x⁴-4x³-3x²+14x-8

500

Solve: x⁴+22x²-75=0

sqrt(3), -sqrt(3), 5i, -5i

Random

100

Find f(g(2)):

f(x)=x²-11

g(x)=3x+4

89

200

Solve:

|x-5|+7=20

x=18, -8

300

Divide:

(1+3i)/(4-5i)

-11/41 +17/41 i

400

Solve: 

2x²+x-15>0

(-infinity, -3) U (5/2, infinity)

500

Find a polynomial function with zeros: 4+i, -2, and 5 that has a leading coefficient of 3.

P(x)=3x⁴-33x³+93x²+87x-510