Graph the function f, left bracket, x, right bracket, equals, minus, 2, log, base, 4, left bracket, x, plus, 1, right bracket, plus, 2f(x)=−2log

Question

4
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(x+1)+2 on the axes below. You must plot the asymptote and any two points with integer coordinates.

Answer 1

We will graph the function f(x) = -2log₄(x+1) + 2.

First, let's find the asymptote. The logarithm function has an asymptote at x = 0, so the function will have a vertical asymptote at x = -1, since we have x + 1 in the logarithm.

Next, let's find two points with integer coordinates. Let's choose x = -2 and x = 0.

When x = -2:
f(-2) = -2log₄(-2+1) + 2 = -2log₄(-1) + 2 = -2 * 0 + 2 = 2.
So we have the point (-2, 2).

When x = 0:
f(0) = -2log₄(0+1) + 2 = -2log₄(1) + 2 = -2 * 0 + 2 = 2.
So we have the point (0, 2).

Now, let's graph the function on the axes:

(Insert graph of f(x) = -2log₄(x+1) + 2 here)

The graph will have a vertical asymptote at x = -1 and passes through the points (-2, 2) and (0, 2).