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

the graph of f is given below. use the graph to determine the following characteristics of f. if a solution does not exist, enter dne. domain: (-∞,∞) range: -1,∞) x - intercept(s) = -4 y - intercept = 4 open interval(s) on which f is increasing: (4,∞) open interval(s) on which f is decreasing: (-∞,-4) open interval(s) on which f is constant: dne any x - value for which f has a relative minimum: -4 the value of any relative minimum of f: any x - value for which f has a relative maximum: the value of any relative maximum of f: f(-10)= the x - value(s) for which f(x)= -1: is f even, odd, or neither? select an answer

the graph of f is given below. use the graph to determine the following characteristics of f. if a solution does not exist, enter dne. domain: (-∞,∞) range: -1,∞) x - intercept(s) = -4 y - intercept = 4 open interval(s) on which f is increasing: (4,∞) open interval(s) on which f is decreasing: (-∞,-4) open interval(s) on which f is constant: dne any x - value for which f has a relative minimum: -4 the value of any relative minimum of f: any x - value for which f has a relative maximum: the value of any relative maximum of f: f(-10)= the x - value(s) for which f(x)= -1: is f even, odd, or neither? select an answer

Answer

Explanation:

Step1: Identify relative minimum value

The relative - minimum occurs at $x = - 4$ and the value of the function at this point is the $y$ - coordinate of the vertex. From the graph, when $x=-4$, $y = - 1$.

Step2: Check for relative maximum

The function has no "hills" in its graph, so there is no relative maximum.

Step3: Find $f(-10)$

Looking at the graph, when $x=-10$, the function value is $3$.

Step4: Find $x$ - values for $f(x)=-1$

The function $y = f(x)$ has a $y$ - value of $-1$ at $x=-4$.

Step5: Determine if the function is even, odd, or neither

A function $y = f(x)$ is even if $f(-x)=f(x)$ (symmetric about the $y$ - axis) and odd if $f(-x)=-f(x)$ (symmetric about the origin). The graph of $y = f(x)$ is not symmetric about the $y$ - axis or the origin, so it is neither.

Answer:

The value of any relative minimum of $f$: $-1$ Any $x$ - value for which $f$ has a relative maximum: DNE The value of any relative maximum of $f$: DNE $f(-10)=3$ The $x$ - value(s) for which $f(x)=-1$: $-4$ Is $f$ even, odd, or neither? Neither