Question

The graph of exponential function f passes through the point (2,4). If g(x)=f(2x), what point is on the graph of function g? A. (2,8) B. (4,4) C. (1.4) D. (2,2)

Answer 1

Answer:

• C. (1, 4)

Step-by-step explanation:

Let's take a simple function:

• f(x) = aˣ

If its graph passes through the point (2, 4), we have:

• f(2) = 4
• a² = 4 ⇒ a = 2

• f(x) = 2ˣ

If g(x) = f(2x), then:

• g(x) = 2²ˣ

If g(x) = 4, then:

• 4 = 2²ˣ ⇒ x = 1 ⇒ the point is (1, 4)

Or g(2) is:

• g(2) = f(4) = 2⁴ = 16 ⇒ the point is (2, 16)

As we see correct choice is C

Answer 2

Answer:C (1,4)

Step-by-step explanation:

When a transformed function is in the form , the graph is stretched or compressed horizontally. When , the curve is compressed horizontally by a factor of .

For function g, , the the graph is compressed by a factor of . Each point on the graph of function g will be half as far from the y-axis as the corresponding point on the graph of function f. Since the point  is on the graph of f, the point  must be on the graph of g.