For the graph of the function f,
(a) Find the domain and the range of f.
(b) Find the intercepts.
(c) Is the graph of f symmetric with respect to the x-axis, the y-axis, or the origin?
(d) Find f (2).
(e) For what value(s) of x is $f (x) = 3$ ?
(f) Solve $f (x) < 0$ .
(g) Graph $y = f (x) + 2$ .
(h) Graph $y = f (- x)$ .
(i) Graph $y = 2 f (x)$ .
(j) Is f even, odd, or neither?
(k) Find the interval(s) on which f is increasing.

Question

For the graph of the function f,
(a) Find the domain and the range of f.
(b) Find the intercepts.
(c) Is the graph of f symmetric with respect to the x-axis, the y-axis, or the origin?
(d) Find f (2).
(e) For what value(s) of x is $f (x) = 3$ ?
(f) Solve $f (x) < 0$ .
(g) Graph $y = f (x) + 2$ .
(h) Graph $y = f (- x)$ .
(i) Graph $y = 2 f (x)$ .
(j) Is f even, odd, or neither?
(k) Find the interval(s) on which f is increasing.

Accepted Answer

(a) The domain of f is $D_{f} = [- 4, 4]$ and the range is $R = [- 1, 3]$

(b) The intercepts are $(- 1, 0), (0, - 1), (1, 0)$

(c) The x coordinates of the corresponding pairs are symmetric with respect to the y-axis, so the f is symmetric with respect to the y-axis.

(d) $f (2) = 1$

(e) The values of x are $(4, 3) \to f (4) = 3 (- 4, 3) \to f (- 4) = 3$

(f) localid="1650165486015" $x \in [- 1, 1]$

(g) The graph is

(h) The graph is

(i) The graph is

(j) The function f is even

(k) The function f is increasing $x \in [0, 4]$

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Step by Step Solution

Step 1. Given information

Part (a) of Step 1. Domain and Range

Part (b) of Step 1. Intercept

Part (c) of Step 1. Is the graph symmetric

Part (d) of Step 1. find f2

Part (e) of Step 1. Value of x if fx=3

Part (f) of Step 1. Solve

Part (g) of Step 1. Graph

Part (h) of Step 1. Graph

Part (i) of Step 1. Graph

Part (j) of Step 1. Is f even, odd, or neither

Part (k) of Step 1. interval(s) on winch f is increasing

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