Investigating Graphs of Even and odd Monomial Functions

Which is the graph of y = -xn where n is odd?

3rd graph

Graph ___ is y = 2x4

A

Which of the following graphs could represent monomial functions? Select all that apply.

A and C

Graph ___ is y = x84

B

Graph ___is y = −5x4

C

Graph several monomial functions where a = 1 and n is odd. For example, y = x3, y = x5, y = x7, and so on. Trace along the functions, then check all of the statements that are true about all of these functions.

The graph is symmetric about the origin. The graph has only 1 y-intercept.

What is the range of the function in this situation?

V(r)>_0

Graph _ is y = −3x8

b

Graph _ is y = 0.25x8

c

As x < 0 decreases, f(x)

decreases

For even monomial functions y = axn where a < 0:As x > 0 increases, f(x)

decreases

For odd power functions, a < 0:As x > 0 increases, f(x) As x < 0 decreases, f(x)

decreases, increases

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.

even, a is negative

Identify the monomial function(s) that have a minimum.

y = 4x4 y = 3x2 y = 2x6 the last 3 answers

On the calculator, graph several monomial functions where a = 1 and n is even. For example, y = x4, y = x6, y = x8, and so on. Trace along the functions, then check all of the statements that are true about all of these functions.

The graph opens up. The graph passes through (0, 0). The graph only has 1 x-intercept.

Which of the following are properties of the graph of an odd monomial function? Select all that apply.

When a > 0, the graph has no minimum or maximum point When a < 0, the graph has no minimum or maximum point. When a < 0, the graph is in Quadrants II and IV. As | a | increases, the graph becomes narrower.

Graph _ is y = x8

a

As x < 0 decreases, f(x)

increases

For even monomial functions y = axn where a > 0:As x > 0 increases, f(x)

increases

For odd power functions, a > 0:As x > 0 increases, f(x) As x < 0 decreases, f(x)

increases, decreases

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.

odd, a is negative

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.

odd, a is positive

The function y = 5x11 is symmetric with respect to the ____

orgin

The formula for the volume of a sphere is a power function:V(r) = r3What is the domain of the function in this situation?

r>_0

The surface area of a cube-shaped gift box can be represented by the function A(s) = 6s2, where s is the side length of the box in inches.What does the constant in the function A(s) represent?

the number of faces on the box

Identify the monomial function(s) that have a maximum.

y = -3x4 y = -2x12 (3rd and 4th/c &d)

The function y = −3x6 is symmetric with respect to the ____

y axis

Marisol has 486 square inches of wrapping paper to cover a gift box. What is the side length of the largest size box she can use to wrap a gift?

9 inches

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.

even, a is positive