Questions: Use the graph to find the following. (a) the domain of f (b) the range of f (c) the x-intercepts (d) the y-intercept (e) intervals on which f is increasing (f) intervals on which f is decreasing (g) intervals on which f is constant (h) the number at which f has a relative minimum (i) the relative minimum of f (j) f(0) (k) The values of x for which f(x)=3 (l) Is f even, odd or neither?

Use the graph to find the following.
(a) the domain of f
(b) the range of f
(c) the x-intercepts
(d) the y-intercept
(e) intervals on which f is increasing
(f) intervals on which f is decreasing
(g) intervals on which f is constant
(h) the number at which f has a relative minimum
(i) the relative minimum of f
(j) f(0)
(k) The values of x for which f(x)=3
(l) Is f even, odd or neither?

Transcript text: Use the graph to find the following. (a) the domain of $f$ (b) the range of $f$ (c) the x-intercepts (d) the $y$-intercept (e) intervals on which $f$ is increasing (f) intervals on which $f$ is decreasing (g) intervals on which $f$ is constant (h) the number at which f has a relative minimum (i) the relative minimum of $f$ (j) $f(0)$ (k) The values of $x$ for which $f(x)=3$ (I) Is $f$ even, odd or neither?

Solution

Solution Steps

Step 1: Determine the domain of f

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the given graph, the function is defined for all real numbers.

Final Answer

The domain of f is $(- \infty, \infty)$.

Step 2: Determine the range of f

The range of a function is the set of all possible output values (y-values). From the graph, the lowest point on the graph is at y = -4, and the function extends upwards indefinitely.

Final Answer

The range of f is $[-4, \infty)$.

Step 3: Determine the x-intercepts

The x-intercepts are the points where the graph crosses the x-axis. From the graph, the function crosses the x-axis at x = -2 and x = 2.

Final Answer

The x-intercepts are $-2$ and $2$.

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