Graphs of Rational Functions Answers

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Which graph represents the rational function ?

Option

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Which statements describe the end behavior of the graph of the function shown? Check all that apply.

As x → ∞, y → 1.

As x → ∞, y → ∞.

As x → ∞, y → –∞.

As x → –∞, y → 1.

As x → –∞, y → ∞.

As x → –∞, y → –∞.

At which values of x does the graph of have a vertical asymptote? Check all that apply.–4–1124

–4

–1

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

At which values of x does the graph of have a vertical asymptote? Check all that apply.

–4

–1

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How would you describe the relationship between the real zero(s) and x-intercept(s) of the function

When you set the function equal to zero, the solution is x = 1; therefore, the graph has an x-intercept of (1, 0).

When you set the function equal to zero, the solutions are x = 0 or x = 1; therefore, the graph has x-intercepts at (0, 0) and (1, 0).

When you substitute x = 0 into the function, there is no solution; therefore, the graph will not have any x-intercepts.

Since there are asymptotes at x = –3, x = –1, and x = 0, the graph has no x-intercepts and, therefore, no real zeros.

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