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 1,3. (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.
find the y - intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the y - intercept(s) is/are. (type an integer or a decimal. use a comma to separate answers as needed.)
b. the graph touches the y - axis on the interval. (type your answer in interval notation.)
c. the graph has no y - intercepts.

Explanation:

Step1: Identify x-intercepts

The graph touches the x-axis at all points from $x=1$ to $x=3$, inclusive, so the x-intercepts are the interval $[1,3]$.

Step2: Identify y-intercepts

The graph does not cross or touch the y-axis (the line $x=0$) at any point, so there are no y-intercepts.

Step3: Check symmetry

• Symmetry about x-axis: For every point $(x,y)$ on the graph, $(x,-y)$ is not present.
• Symmetry about y-axis: For every point $(x,y)$ on the graph, $(-x,y)$ is not present.
• Symmetry about origin: For every point $(x,y)$ on the graph, $(-x,-y)$ is not present.

Thus, the graph has none of these symmetries.

Answer:

(a)
X-intercept: A. The graph touches the x-axis on the interval $[1,3]$.
Y-intercept: C. The graph has no y-intercepts.
(b)
None of these.