2.7, 2.8, 3.1 Review

Quadratic Functions

100

What is the vertex of the following quadratic function?

y=(x+2)^2-7

(-2, -7)

200

If the vertex is (4, -5), what is the Axis of Symmetry?

x=4

300

Does the following quadratic function have a maximum or minimum? What is that max or min value?

y=-3(x+2)^2-4

Maximum Value of -4

400

Does the following quadratic function have a maximum or minimum? What is that max or min value?

y=1/2x^2+3

Minimum Value of 3

500

Write the equation of a parabola with the given vertex.

Vertex: (-3, 7)

f(x)= a(x+3)²-7

(a can be any constant)

Piecewise Functions

100

Evaluate the following piecewise function at the indicated values. 

f(x)= 8x+3, if x>2 

f(x)= (1/2)x-1, if x≤2 

Find f(-3)

-2.5

200

Evaluate the following piecewise function at the indicated values. 

f(x)= 8x+3, if x>2 

f(x)=(1/2)x-1, if x≤2 

Find f(5)

43

300

Evaluate the following piecewise function at the indicated values. 

f(x)= 8x+3, if x>2 

f(x)=(1/2)x-1, if x≤2 

Find f(2)

0

400

Evaluate the following piecewise function at the indicated values. 

f(x)= -x-7, if x≤2 

f(x)=(3/2)x+3, if x>2 

Find f(5)

10.5

500

Evaluate the following piecewise function at the indicated values. 

f(x)= -x-7, if x≤2 

f(x)= 8, if 2<x≤4

f(x)=3/2x+3, if x>4

Find f(-1)

-6

Symmetry

100

Is the function f(x)=x²+2x-3 even, odd, or neither?

neither

200

Is the function f(x)=x²-3 even, odd, or neither?

even

300

Is the function f(x)=9x⁴-2x² symmetric to the x-axis, y-axis, origin, or none of these?

y-axis

400

Is the function f(x)= -3x+5 even, odd, or neither?

neither

500

Is the function graphed even, odd, or neither?

odd

Function Operations

100

Using the following functions perform the operation f(x)=3x+5 and g(x)=2x-3 : f(x)+g(x)

5x+2

200

Using the following functions perform the operation f(x)=3x+5 and g(x)=2x-3 : f(x)-g(x)

x+8

300

Using the following functions perform the operation f(x)=3x+5 and g(x)=2x-3 : f(x)/g(x)

3x+5/ 2x-3

400

Using the following functions perform the operation f(x)=3x+5 and g(x)=2x-3 : (f*g)(2)

11

500

Using the following functions perform the operation f(x)=3x and g(x)=x-5 : f(x) / g(x)

3x/x-5

Compositions

100

Let f(x)=x+5 and g(x)=2x²-1 : f(f(x))

x+10

200

Let f(x)=x+5 and g(x)=2x²-1 : g(f(x))

2x²+20x+49

300

Let f(x)=x+5 and g(x)=2x²-1 : f(g(x))

2x²+4

400

Let f(x)=6x and g(x)=3x+5 : f(g(x))

18x+30

500

Let f(x)=6x and g(x)=3x+5 : g(f(-1))

-13