Answer:
On a coordinate plane, an exponential function increases in
quadrant 3 into quadrant 4 and approaches y = 0. It goes through
(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The function
is reflected across the
y-axis and then across the x- axis
- Lets revise the reflection of a function across the axes
- If the function f(x) reflected across the x-axis, then the new function
h(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new function
g(x) = f(-x)
∵
is reflected across the y-axis
- Change the sign of x
∴ Its image is g(x) where ![g(x)=\frac{1}{4}(8)^{-x}](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%288%29%5E%7B-x%7D)
∵
is reflected across the x-axis
- Change the sign of y
∴ Its image is h(x) where ![h(x)=-\frac{1}{4}(8)^{-x}](https://tex.z-dn.net/?f=h%28x%29%3D-%5Cfrac%7B1%7D%7B4%7D%288%29%5E%7B-x%7D)
∴ h(x) is the image of f(x) after reflected across the y-axis then
reflected across the x-axis
* Look to the attached graph for more understand
- f(x) represented by red
- g(x) represented by blue
- h(x) represented by green
* From the graph
- The green graph is in the 3rd and 4th quadrants
- Approaches y = 0 (x-axis)
- point (-1 , -2) lies on it
- It cross the y-axis at point (0 , -0.25)
∴ The answer is the last one
On a coordinate plane, an exponential function increases in
quadrant 3 into quadrant 4 and approaches y = 0. It goes through
(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25)