Question

Question 1.

Answer 1

Answer:

1. f(x) = g(x - 4)

2. g(x) = f(x + 4)

3. y = (-3/2)x + 4

4. y = (-3/2)x - 2

Step-by-step explanation:

1. Notice that the point (0, -2) lies on g(x) and the point (4, -2) lies on f(x). That means the translation function from g(x) to f(x) is 4 units to the right. So, we have: f(x) = g(x - 4).

2. This one is kind of the opposite of number 1; g(x) is 4 units to the left of f(x), so we have: g(x) = f(x + 4).

3. Slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept. Slope is change in y over change in x, so pick any two points on the line of f: (0, 4) and (4, -2).

slope = m = (4 - (-2)) / (0 - 4) = 6/(-4) = -3/2

The y-intercept is where the graph crosses the y-axis, which is (0, 4), so b = 4. Then:

y = (-3/2)x + 4

4. Pick any two points to find the slope: (-4, 4) and (0, -2).

slope = m = (4 - (-2)) / (-4 - 0) = 6/(-4) = -3/2

The y-intercept is at (0, -2), so b = -2. Then:

y = (-3/2)x - 2

Answer 2

Answer:

Q1) f(x) = g(x) + 6

Q2) g(x) = f(x) - 6

Q3) f(x) = (-3/2)x + 4

Q4) g(x) = (-3/2)x - 2

Step-by-step explanation:

g(x) is 6 units vertically below f(x)

Slope: (1-4)/(2-0) = -3/2

f(x) = (-3/2)x + 4

g(x) = (-3/2)x - 2