Questions: 5. In the space provided, label each function as even, odd, or neither. a) f(x) = x^4 - 5 b) f(x) = x^4 + x c) f(x) = -2x^3 7. Sketch a graph of the following functions a) f(x) = x - 2 b) f(x) = sqrt(x) + 1 c) f(x) = (x + 2)^2 - 3 d) f(x) = -x 8. Write the function whose graph is the graph of f(x) = sqrt(x), but is a) shifted left 3 b) shifted down 5 c) reflected over the y-axis d) shifted right 1

5. In the space provided, label each function as even, odd, or neither.
a) f(x) = x^4 - 5
b) f(x) = x^4 + x
c) f(x) = -2x^3

7. Sketch a graph of the following functions
a) f(x) = x - 2
b) f(x) = sqrt(x) + 1
c) f(x) = (x + 2)^2 - 3
d) f(x) = -x

8. Write the function whose graph is the graph of f(x) = sqrt(x), but is
a) shifted left 3
b) shifted down 5
c) reflected over the y-axis
d) shifted right 1

Transcript text: 5. In the space provided, label each function as even, odd, or neither. a) $f(x)=x^{4}-5$ $\qquad$ b) $f(x)=x^{4}+x$ $\qquad$ c) $f(x)=-2 x^{3}$ 7. Sketch a graph of the following functions a) $f(x)=|x-2|$ b) $f(x)=\sqrt{x}+1$ c) $f(x)=(x+2)^{2}-3$ d) $f(x)=-|x|$ 8. Write the function whose graph is the graph of $f(x)=\sqrt{x}$, but is a) shifted left 3 b) shifted down 5 c) reflected over the $y$-axis d) shifted right 1

Solution

Solution Steps

Step 1: Analyzing function a)

To determine if $f(x) = x^4 - 5$ is even, odd, or neither, we evaluate $f(-x)$: $f(-x) = (-x)^4 - 5 = x^4 - 5 = f(x)$. Since $f(-x) = f(x)$, the function is even.

Step 2: Analyzing function b)

For $f(x) = x^4 + x$, we have: $f(-x) = (-x)^4 + (-x) = x^4 - x$. Since $f(-x)$ is not equal to $f(x)$ or $-f(x)$, the function is neither even nor odd.

Step 3: Analyzing function c)

For $f(x) = -2x^3$, we have: $f(-x) = -2(-x)^3 = -2(-x^3) = 2x^3 = -(-2x^3) = -f(x)$. Since $f(-x) = -f(x)$, the function is odd.