Question

the graph of an equation is shown on the right.
(a) find the intercepts.
(b) indicate whether the graph is symmetric with respect to the x - axis, the y - axis, the origin, or none of these.
(a) find the x - intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the graph touches the x - axis on the interval
(type your answer in interval notation.)
b. the x - intercept(s) is/are
(type a whole number. use a comma to separate answers as needed.)
c. the graph has no x - intercepts.

Explanation:

Step1: Identify x-intercept interval

The graph touches the x-axis between $-5$ and $0$, inclusive, as shown by the solid segment on the x-axis from $-5$ to $0$.
Interval notation: $[-5, 0]$

Step2: Identify y-intercept

The graph crosses the y-axis at $(0,0)$, so the y-intercept is $0$.

Step3: Check symmetry

• X-axis symmetry: A point $(x,y)$ on the graph has no corresponding $(x,-y)$ point, so no x-axis symmetry.
• Y-axis symmetry: A point $(x,y)$ on the graph has no corresponding $(-x,y)$ point, so no y-axis symmetry.
• Origin symmetry: A point $(x,y)$ on the graph has no corresponding $(-x,-y)$ point, so no origin symmetry.

Answer:

(a)

X-intercept: A. The graph touches the x-axis on the interval $[-5, 0]$
Y-intercept: $0$

(b)

None of these