Exploring Power Functions

8

4

10

6

The graph of f(x) = x^2 is a parabola that opens upwards.

The graph of f(x) = x^2 is a circle.

The graph of f(x) = x^2 is a straight line.

The graph of f(x) = x^2 opens downwards.

odd function

maximum at (0,0)

Characteristics of f(x) = x^4: even function, degree 4, minimum at (0,0), continuous, differentiable, approaches infinity as |x| increases.

degree 3

3

4

2

5

f(x) = (x + 1)^2 + 3 shifts the graph left by 1 unit.

f(x) = (x - 1)^2 - 3 shifts the graph down by 3 units.

f(x) = (x + 1)^2 - 3 shifts the graph left by 1 unit and down by 3 units.

f(x) = (x - 1)^2 + 3 is a transformation that shifts the graph of y = x^2 to the right by 1 unit and up by 3 units.

2

0

-2

-1

The function f(x) = x^(-2) has a vertical asymptote at x = 1.

The function f(x) = x^(-2) has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

The function f(x) = x^(-2) has no asymptotes.

The function f(x) = x^(-2) approaches y = 1 as x approaches infinity.

7

6

8

5

x = 1

x = 0

x = 2 or x = -2

x = 4

f(x) = -x^2 + 2 transforms x values into new y values.

f(x) = -x^3 + 2 transforms x values into new y values.

f(x) = -2x^3 + 2 transforms x values into new y values.

f(x) = x^3 + 2 transforms y values into new x values.