Question

The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.

Answer 1

The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.

Step-by-step explanation:

To vertically compress the parent function f(x) = 5x by a factor of one-half, we multiply the function by the compression factor, which is 1/2. So the compressed function is f(x) = (1/2)(5x) = 2.5x.

To shift the function to the left three units, we subtract the shift amount from the x-variable. So the shifted function is f(x + 3) = 2.5(x + 3) = 2.5x + 7.5.

To shift the function up two units, we add the shift amount to the y-variable. So the final transformed function is f(x + 3) + 2 = 2.5x + 7.5 + 2 = 2.5x + 9.5.

Answer 2

We are given the parent function, f(x) = 5x and is vertically compressed by a factor of 1/2, shifted to the right (3 units) and down two units.

Vertical compression makes the function:

f(x) = (1/2) * 5x

shifted 3 units to the right makes the function:

f(x) = (1/2) * 5 (x+3)

shifted 2 units down makes the function:

f(x) = (1/2) *(5 (x+3)) - 2

therefore, this function is the resulting function after performing all three adjustments of the parent function. First, compression, then shift to left/right, then shift up and down.