the graph of f is given below. use the graph to determine the following characteristics of f. if a solution…

Explanation:

Step1: Determine domain

The graph exists for all real - x values. So the domain is all real numbers, $(-\infty,\infty)$.

Step2: Determine range

The lowest y - value is $y = - 1$ and it goes up to $\infty$. So the range is $[-1,\infty)$.

Step3: Find x - intercepts

The graph crosses the x - axis at $x=-4$. So the x - intercept is $x = - 4$.

Step4: Find y - intercept

The graph crosses the y - axis at $y = 4$. So the y - intercept is $y = 4$.

Step5: Find increasing intervals

The graph is rising for $x>-4$. So the increasing interval is $(-4,\infty)$.

Step6: Find decreasing intervals

The graph is falling for $x < - 4$. So the decreasing interval is $(-\infty,-4)$.

Step7: Find constant intervals

The graph is not flat anywhere, so the constant interval is DNE.

Step8: Find x - value for relative minimum

The relative minimum occurs at the lowest point of the graph, which is at $x=-4$.

Answer:

Domain: $(-\infty,\infty)$ Range: $[-1,\infty)$ $x$-intercept(s): $x = - 4$ $y$-intercept: $y = 4$ Open interval(s) on which $f$ is increasing: $(-4,\infty)$ Open interval(s) on which $f$ is decreasing: $(-\infty,-4)$ Open interval(s) on which $f$ is constant: DNE Any $x$-value for which $f$ has a relative minimum: $x=-4$