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 (square). (type your answer in interval notation.)
b. the x - intercept(s) is/are (square). (type a whole number. use a comma to separate answers as needed.)
c. the graph has no x - intercepts.

Explanation:

Step1: Identify x-intercepts

The x-intercept is where the graph crosses/touches the x-axis (y=0). From the graph, the graph touches/crosses the x-axis at $x=3$ and $x=1$, and the line segment lies on the x-axis between these points.

Step2: Determine interval for x-axis touch

The graph lies on the x-axis between $x=1$ and $x=3$, so the interval is $[1, 3]$.

Step3: Check symmetry

• X-axis symmetry: A point $(x,y)$ has a mirror $(x,-y)$ on the graph. The graph has points above the x-axis, no corresponding points below, so no x-axis symmetry.
• Y-axis symmetry: A point $(x,y)$ has a mirror $(-x,y)$ on the graph. The graph is only on the right side of the y-axis, no mirror points on the left, so no y-axis symmetry.
• Origin symmetry: A point $(x,y)$ has a mirror $(-x,-y)$ on the graph. No such mirrored points exist, so no origin symmetry.

Answer:

(a) A. The graph touches the x-axis on the interval $[1, 3]$.
(b) None of these