Question

For the basic function f(x) = x, what conclusions can you make about fix) and

f(x) - 5? Select all that apply.

a. They intercepts are the same.
b. The function () - 5 has a greater rate
of change
c. They are parallel lines:
d. The graph of the function(x) is translated
down 5 units to produce fix) - 5.

Answer 1

c, d

Explanation:

If f(x) = x, then f(x) - 5 = x - 5.

The two functions in slope-intercept form (y = mx+ b) are:

[1] y = x and [2] y = x - 5

In equation [1], the slope is 1 and the y-intercept is 0.

In equation [2], the slope is 1 and the y-intercept is -5.

a. The y-intercepts are not the same. 0 ≠ -5

b. The rates of change, or the slopes, are the same, neither are greater than the other. 1 = 1

c. They are parallel lines. Lines are parallel when they have the same slope. 1 = 1.

d. The (-5) indicates that the new function is translated down (-) by 5 units (5) from the parent function f(x) = x.

c and d are correct.