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