122k views
0 votes
State the domain range intercepts) and asymptotes) of y=-2^(-x+2) + .1

User Zhangv
by
8.7k points

1 Answer

2 votes

Final Answer:

The given function is y = -2^(-x+2) + 0.1. The domain is all real numbers, the range is y ≤ 0.1, the y-intercept is (0, -3.9), and there are no x-intercepts. The function has a horizontal asymptote at y = 0.1 and approaches it as x goes to positive or negative infinity.

Step-by-step explanation:

Domain: The function is defined for all real numbers.

Range: The range is y ≤ 0.1 since 2^(-x+2) is always positive or zero.

Y-intercept: Substitute x = 0 to find the y-intercept: y = -2^2 + 0.1 = -3.9, so the y-intercept is (0, -3.9).

X-intercept: Set y = 0 and solve for x, but there are no real solutions, so no x-intercepts.

Asymptote: The function approaches y = 0.1 as x goes to positive or negative infinity.

User Sonnie
by
7.7k points