Question

F(x) = 2x - 3. What is the new function k(x) after a vertical compression by a factor of 0.7?

A. k(x) = 0.7(2x - 3)
B. k(x) = 2(0.7x) - 3
C. k(x) = 2x - 3
D. k(x) = 2x - 0.7

Let g(x) be the indicated transformation of f(x) = x. Write the rule for g(x) after a vertical translation down 2 units.
A. g(x) = x - 2
B. g(x) = x + 2
C. g(x) = x - 0.7
D. g(x) = x - 3

Let h(x) be the indicated transformation of f(x) = x. Write the rule for h(x) after a horizontal stretch by a factor of 3.
A. h(x) = 3x
B. h(x) = x / 3
C. h(x) = x * 3
D. h(x) = 3 / x

Answer 1

The new function after vertical compression is

A. k(x) = 0.7(2x - 3)

The rule for g(x) after a vertical translation down 2 units is

A. g(x) = x - 2

The rule for h(x) after a horizontal stretch by a factor of 3 is

A. h(x) = 3x

Vertical Compression

vertical compression of a function f(x) by a factor a is given by k(x) = a f(x). In this case, a = 0.7.

So, the correct answer is:

A. k(x) = 0.7(2x - 3)

Vertical translation down 2 units:

vertical translation down by b units is given by g(x) = f(x) - b. In this case,b = 2

So, the correct answer is:

A. g(x) = x - 2

Horizontal stretch by a factor of 3.

A horizontal stretch of a function f(x) by a factor c is given by h(x) = f(cx). In this case, c = 3.

the correct answer is:

A. h(x) = 3x