Question

answer the following questions about the graph of the function ( g(x) ) shown below.
a) what are the ( y )-intercept(s)?
b) what are the ( x )-intercept(s)?
c) is ( g(x) ) increasing or decreasing on the interval ( 0 < x < 2 )?
d) does the graph have a minimum, maximum, both or neither? if so, where are these points?
e) what is ( g(-3) )?

Explanation:

Step1: Identify y-intercept (x=0)

The y-intercept is where the graph crosses the y-axis ($x=0$). From the graph, this point is $(0, -4)$.

Step2: Identify x-intercepts (y=0)

The x-intercepts are where the graph crosses the x-axis ($y=0$). From the graph, these points are $(-2, 0)$ and $(2, 0)$.

Step3: Analyze interval $0

On $0

Step4: Identify extrema of parabola

The graph is an upward-opening parabola, so it has a minimum (no maximum). The vertex (minimum point) is at $(0, -4)$.

Step5: Find $g(-3)$ from graph

Locate $x=-3$ on the graph; the corresponding $y$-value is 5, so $g(-3)=5$.

Answer:

a) The y-intercept is $(0, -4)$
b) The x-intercepts are $(-2, 0)$ and $(2, 0)$
c) $g(x)$ is increasing on $0d) The graph has a minimum at the point $(0, -4)$ (no maximum)
e) $g(-3)=5$