Question

Given the following function, name the Key Point: f(x) = 4 + log₂(x + 3)

A) The logarithmic rule
B) The exponential function
C) The y-intercept
D) The base of the logarithm
E) None of the above.

Answer 1

The key point given in the function f(x) = 4 + log2(x + 3) is the y-intercept, which is found by setting x to 0. The y-intercept is at the point (0, 4 + log2(3)) on the graph of the function, making the answer 'C) The y-intercept'.

Step-by-step explanation:

The key point given in the function f(x) = 4 + log2(x + 3) is the y-intercept. The y-intercept is the point where the graph of the function crosses the y-axis. To find the y-intercept, we set x to 0. However, we need to make sure that the input to the logarithmic function is positive because the logarithm is not defined for non-positive numbers. In this case, when x is 0, the input to the logarithm is x + 3 = 3, which is indeed positive, so we can proceed.

The y-intercept is f(0) = 4 + log2(3). Since the specific value of log2(3) isn't pertinent to naming the point, the y-intercept is determined by the constant added to the logarithm, in this case, 4. Therefore, the correct answer to the question is 'C) The y-intercept', which is the point (0, 4 + log2(3)) on the graph of the function