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Ket [755]
1 year ago
12

Four functions are given below. Either the function is defined explicitly, or the entire graph of the function is shown.For each

, decide whether it is an even function, an odd function, or neither.

Mathematics
1 answer:
Masja [62]1 year ago
4 0

Summary of even and odd functions

A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.

A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f.

From the definition itself, we see how can we test if the functions are even or odd.

- First graph (to the left)

From the graph, we see that the function is symmetric with respect to the y-axis because the left side (x<0) is a reflection (along the y-axis) of the right side (x>0), so it is an even function.

- Second graph (to the right)

From the graph, we see that the function is symmetric with respect to the origin, the left side (x<0) is a reflection (along with the origin) of the side to the right (x>0), so it is an odd function.

- First function (to the left)

The function:

g(x)=5x^2

is an even function because we see that:

g(-x)=5\cdot(-x)^2=5x^2=g(x)

- Second function (to the right)

The function:

h(x)=-2x^5+3x^3

is an odd function because we see that:

h(-x)=-2\cdot(-x)^5+3\cdot(-x)^3=-(-2x^5+3x^3)=-h(x)^{}

Summary

We have the following results:

- First function (to the left): even

- Second graph (to the right): odd

- First function (to the left): even

- Second function (to the right): odd

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