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:
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