Question

Determine whether the graph is that of a function by using thevertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or theorigin(4. - 1)Is the graph that of a function?

Answer 1

In this problem, we have a vertical parabola open upward with vertex at (4,-1)

so

Applying the vertical line test

we have that

For one value of x, there is only one value of y

that means

The graph represents a function

therefore

Is the graph a function? ----------> Yes

Find out the domain

the domain is all real numbers ------> interval (-infinite, infinite)

Find out the range

The range is the interval [-1, infinite)

Find out the intercepts

y-intercept ------> (0,5)

x-intercepts -----> about (3,0) and (5,0)

axis of symmetry

x=4

the graph is symmetry with the line x=4