Question

PLS HELP WITHIN 5 MINS

What key features does f(x), shown in the graph, share with g(x), shown in the equation? Select three options.

at least one x-intercept
at least one y-intercept
an oblique asymptote
a vertical asymptote
the domain of x

Answer 1

(a) at least one x-intercept

(b) at least one y-intercept

(e) the domain of x

Explanation:

Given g(x) = (-4x² +36)/(x+3) and f(x) as shown in the graph, you want to know what features the functions have in common.

G(x)

The function g(x) can be simplified:

`g(x)=(-4x^2+36)/(x+3)=(-4(x^2 -9))/(x+3)=(-4(x+3)(x-3))/(x+3)\\\\g(x)=-4(x-3)\quad x\\e-3`

This is the equation of a straight line with negative slope and a hole at coordinates (-3, 24). That is, the domain excludes x = -3.

The line has x-intercept (3, 0) and y-intercept (0, 12).

Common features

Both functions have an x-intercept at (3, 0), at least one x-intercept, choice A.

Both functions have a y-intercept at (0, 12), at least one y-intercept, choice B.

Only function f(x) has an oblique asymptote.

Only function f(x) has a vertical asymptote.

Both functions exclude x = -3 from their domains, so they have the same domain, choice E.

Choices A, B, E identify the shared features.

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