Question

Write an equation that represents the transformations formed by the following items:

a) Horizontally shifting the graph 4 units to the left of f(x) = √x and then vertically compressing by a factor of 1/3.
b) Vertically stretching the graph by a factor of 4 of f(x) = √x and then vertically shifting the graph 3 units up.
c) Horizontally stretching the graph of f(x) = √x by a factor of 2 and then vertically shifting the graph 6 units down.
A) Insert equations for each transformation.
B) Use mathematical symbols for transformations.
C) Describe transformations without equations.
D) Leave transformations unexplained.

Answer 1

a) Horizontally shifting the graph 4 units to the left of f(x) = √x and then vertically compressing by a factor of 1/3: f(x) = (1/3)√(x-4). b) Vertically stretching the graph by a factor of 4 of f(x) = √x and then vertically shifting the graph 3 units up: f(x) = 4√x + 3. c) Horizontally stretching the graph of f(x) = √x by a factor of 2 and then vertically shifting the graph 6 units down: f(x) = √(x/2) - 6.

Step-by-step explanation:

a. Horizontally shifting the graph 4 units to the left of f(x) = √x and then vertically compressing by a factor of 1/3

To horizontally shift the graph 4 units to the left of f(x) = √x, we subtract 4 from the x-value. The equation becomes f(x) = √(x-4). To vertically compress the graph by a factor of 1/3, we multiply the function by 1/3. The final equation is f(x) = (1/3)√(x-4).

b. Vertically stretching the graph by a factor of 4 of f(x) = √x and then vertically shifting the graph 3 units up

To vertically stretch the graph by a factor of 4, we multiply the function by 4. The equation becomes f(x) = 4√x. To vertically shift the graph 3 units up, we add 3 to the function. The final equation is f(x) = 4√x + 3.

c. Horizontally stretching the graph of f(x) = √x by a factor of 2 and then vertically shifting the graph 6 units down

To horizontally stretch the graph by a factor of 2, we divide the x-value by 2. The equation becomes f(x) = √(x/2). To vertically shift the graph 6 units down, we subtract 6 from the function. The final equation is f(x) = √(x/2) - 6.