Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
2 answers:
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
∵ is reflected across the x-axis
- Change the sign of y
∴ Its image is h(x) where
∴ 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)
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