Question

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(-6) (k) the values of x for which f(x)=3 (4,∞) (type your answer in interval notation.) (f) over what interval is f decreasing? (-∞,4) (type your answer in interval notation.) (g) over what interval is f constant? 0 (type your answer in interval notation.) (h) what is the number at which f has a relative minimum? 4 (i) what is the relative minimum of f? -4 (j) what is f(-6)? f(-6)= (k) what are the x - values where f(x)=3? the leftmost x - value where f(x)=3 is when x = 1. what is the rightmost x - value where f(x)=3? x=

Explanation:

Step1: Locate \(x = - 6\) on the graph

Find the value of the function \(y = f(x)\) when \(x=-6\).

Step2: Read the \(y\) - coordinate

From the graph, when \(x = - 6\), the \(y\) - coordinate (i.e., the value of \(f(-6)\)) is \(6\).

Step3: For \(f(x)=3\)

Locate the points on the graph where \(y = 3\). We know one \(x\) value is \(x = 1\). Looking at the graph, when \(y = 3\), the right - most \(x\) value is \(x=9\).

Answer:

\(f(-6)=6\)

The right - most \(x\) value for which \(f(x) = 3\) is \(x = 9\)