Answer:
The corresponding point for the function f(3/4 x) is (12 , -8)
Explanation:
* Lets revise the horizontal stretch or compress
- A horizontal stretching is the stretching of the graph away from
the y-axis
- A horizontal compression is the squeezing of the graph toward
the y-axis.
# if k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally
compressed by dividing each of its x-coordinates by k.
# if 0 < k < 1 (a fraction), the graph y = f(k·x) is the graph of f(x)
horizontally stretched by dividing each of its x-coordinates by k.
* Now lets solve the problem
- The function f(x) will be the function f(3/4 x)
∵ The x multiplied by a constant
∴ f(x) stretched or compressed horizontally
∵ f(x) ⇒ f(k · x)
∵ f(x) ⇒ f(3/4 x)
∴ k = 3/4 ⇒ less than 1
∵ 0 < k < 1
∴ f(x) starched horizontally
∴ Divide each of its x-coordinates by k
∵ k = 3/4
∴ Divide each of its x-coordinates by 3/4
∵ Point (9 , -8) is on the graph of f(x)
- Find the corresponding point on the graph f(3/4 x) by dividing
x-coordinate by 3/4
∵ x = 9
∴ The corresponding x = 9 ÷ 3/4 = 9 × 4/3 = 36/3 = 12
∴ The corresponding point is (12 , -8)