Question

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Q.12
A student was asked to determine the y-intercept for the logarithmic function f (x) = log3(x + 2) + 1. Which of the following expressions would result in the correct y-intercept?

A. the quantity log 2 over log 3 end quantity plus 1
B. the quantity log 3 over log 2 end quantity plus 1
C. 3–1 – 2
D. (–1)3 – 2

Answer 1

The y-intercept of a logarithmic function is the point at which the graph intersects with the y-axis. To find the y-intercept of the given logarithmic function f(x) = log3(x + 2) + 1, we need to substitute x = 0 into the equation and solve for y.

f(0) = log3(0 + 2) + 1
f(0) = log3(2) + 1

Using the change of base formula, we can convert this expression to a common logarithm:

f(0) = log(2)/log(3) + 1

Therefore, the correct expression for the y-intercept is option A: the quantity log 2 over log 3 end quantity plus 1.