Question

Which describes the transformation of the graph f(x) = x + 10 to the graph of g(x) = x - 15?

Options:
1. Rotation (more steep).
2. Rotation (less steep).
3. Translation (down 15).
4. Translation (down 25).

Answer 1

Answer: 4. Translation (down 25).

Proof

f(x) = x+10

g(x) = f(x) - 25

g(x) = (x+10) - 25

g(x) = x - 15

Another proof:

The point (0,10) is on f(x). The corresponding point directly below it on g(x) is (0,-15). Both are y intercepts.

To move from 10 to -15 on the y axis, we move down 25 units. The gap from 10 to 0 is 10, the gap from 0 to -15 is 15, so the total distance is 10+15 = 25 units downward. Therefore, we shift every point on f(x) down 25 units to arrive at a corresponding point on g(x).

Answer 2

The transformation from f(x) = x + 10 to g(x) = x - 15 is a translation downward by 15 units, representing a shift of the graph down the y-axis without changing its slope.

Step-by-step explanation:

The transformation of the graph f(x) = x + 10 to the graph of g(x) = x - 15 involves changing the y-intercept of the line. According to the information provided, if a line has a smaller intercept, it will shift in (or down), parallel to the old line without changing the slope.

Therefore, the correct transformation described is not a rotation but a translation downward by 15 units. Hence, the correct answer is option 3, Translation (down 15).