Question

What transformations are applied to the graph of the function f(x) = 10^x to produce the graph of the function g(x) = 3(10)^x – 2?

A. a vertical dilation by a factor of 1/3 and a vertical shift down 2 units
B. a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
C. a vertical dilation by a factor of 3 and a vertical shift down 2 units
a vertical dilation by a factor of and a horizontal shift to the right 2 units
OB.
OC.
OD

Answer 1

To me I would say A it can’t be b or c

Answer 2

The correct answer is C. a vertical dilation by a factor of 3 and a vertical shift down 2 units.

Let's analyze the given functions and their transformations.

The original function is f(x)=10^x , and the transformed function is g(x)=3(10) x^−2.

Vertical Dilation/Compression: If ∣a∣>1, the graph is vertically compressed. If 0<∣a∣<1, the graph is vertically stretched.

Vertical Shift: Adding or subtracting a constant term inside the function shifts the graph vertically.

Horizontal Shift: Adding or subtracting a constant term outside the function parentheses shifts the graph horizontally.

Now, let's compare the given functions and their transformations:

The coefficient in front of 10^x in g(x) is 3, which means there is a vertical dilation by a factor of 3.

The constant term -2 means a vertical shift down 2 units.

So, the correct answer is C. a vertical dilation by a factor of 3 and a vertical shift down 2 units.