Question

Using the basic function, f(x) = /x/, produce a function rule that will produce a vertical compression by a

factor of 2 and a horizontal translation of 3. Also, identify the y-intercept, the domain, and the range of the
new function.
a) equation:
b) y-intercept:
c) domain:
d) range:

Answer 1

To produce a vertical compression by a factor of 2 and a horizontal translation of 3 for the basic function f(x) = |x|, modify the equation to g(x) = |x|/2 and h(x) = |x - 3|/2. The y-intercept is (0, 1). The domain is (-∞, ∞) and the range is [0, ∞).

Step-by-step explanation:

To produce a vertical compression by a factor of 2 and a horizontal translation of 3 for the basic function f(x) = |x|, you will need to modify the equation. To vertically compress by a factor of 2, divide the function by 2: g(x) = |x|/2. To horizontally translate by 3 units to the right, subtract 3 from x: h(x) = |x - 3|/2.

The y-intercept of the new function can be found by evaluating h(0) which gives us 1. So, the y-intercept is (0, 1).

The domain of h(x) is the set of all real numbers because there are no restrictions on x when taking the absolute value. So, the domain is (-∞, ∞).

The range of h(x) is the set of all real numbers greater than or equal to 0 because the absolute value function is always non-negative. So, the range is [0, ∞).