Question

The sum and product of two linear functions are shown.

Which statements can be used to describe the original functions f(x) and g(x)? Select three options.

When added, the sum of the y-intercepts must be 8.
When multiplied, the product of the y-intercepts must be 8.
Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of –3.
f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –1.

Answer 1

The statements can be used to describe the original functions f(x) and g(x) are;  Option B

How to interpret function graphs?

Let the functions be

f(x) = ax + b

g(x) = cx + d

Their sum is;

j(x) = (a + c)x + b + d

Their product is;

k(x) = (ax + b)(cx + d)

From the graph, we see that;

f(x) = x + 6

g(x) = -2x² + 8

f'(x) = 1

g'(x) = -4x

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