Question

Suppose f(x) = 2x - 4. Describe how the graph of g compares with the graph of f.

g(x) = {(x + 5)
Select the correct choice below, and fill in the answer box to complete your choice.
O A. g(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is stretched horizontally.
O B. The graph of g(x) is translated unit(s) to the right compared to the graph of f(x).
O C. The graph of g(x) is translated unit(s) down compared to graph of f(x).
O D. The graph of g(x) is translated unit(s) to the left compared to the graph of f(x).
O E. g(x) has a scale factor of compared to f(x). Because it scales the vertical direction, the graph is compressed vertically.
O F. 9(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is compressed horizontally.
O G. a(x) has a scale factor of comnared to fly) Because it scales the vertical direction. the graph is stretched vertically.
• H. The graph of g(x) is translated unit(s) up compared to graph of f(X).

Answer 1

The graph of g(x) = 2(x + 5) - 4 is translated 6 units up compared to the graph of f(x) = 2x - 4 because the only difference is the constant term, which is 10 units higher in g(x).

Step-by-step explanation:

We need to consider the function g(x) = 2(x + 5) - 4. If we expand this, we get g(x) = 2x + 10 - 4, which simplifies to g(x) = 2x + 6. Comparing this to f(x) = 2x - 4, we can see that the only difference between f(x) and g(x) is the constant term at the end of the function.

Changing the constant term in a linear function results in a vertical translation of the graph. Since the constant term in g(x) is greater by 10 units than the constant term in f(x), this means that the graph of g(x) is shifted up by 10 units relative to the graph of f(x).

Therefore, the correct choice is:

O H. The graph of g(x) is translated 6 unit(s) up compared to the graph of f(x).

Answer 2

D. The graph of g(x) is translated 5 units to the left compared to the graph of f(x).