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What are the y-intercept and the asymptote of g(x) = 2x – 3?

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Answer:

y-intercept: -3

asymptote: (0, -3)

Explanation:

The asymptote and y-intercept are -3 because you are subtracting 2x, the leading term, by 3, which gives you -3 for this case.

The y-intercept of g(x) is (0, -3) and there are no asymptotes for g(x).

The function is given as g(x) = 2x - 3 and we need to find the y-intercept and the asymptote of this function g(x).

What are the y-intercept and asymptotes of a given function?

Y-intercepts of a given function are the points on the y-axis that the given function passes through.

In y-intercept points we always have x=0.

Asymptotes are straight lines on the graph that meets the given function as it moves towards infinity.

Asymptotes occur only when the given function is a rational function or when one term of the function approaches zero as one term approaches infinity.

Find the y-intercept of g(x).

We have,

g(x) = 2x - 3

Since x = 0.

we get,

g(x) = 0 - 3

g(x) = -3 or y = -3

Thus the y-intercept of g(x) is (0, -3)

Find the asymptotes of g(x).

We see that g(x) is not a rational function and when x approaches infinity g(x) does not approach zero.

Hence we can say that g(x) has no asymptotes.

The y-intercept and asymptotes of g(x) are (0, -3) and no asymptotes.

Learn more about asymptotes of a given function here:

https://brainly.com/question/27861449

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