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
