Question

The parent function of a graph is f(x)=3(2)x

Samantha reflected the parent function over the x-axis to get the following function: g(x)=3(2)−x
a. Describe Samantha's error (2 points)

b. Write the correct equation for g(x) after f(x) has been reflected over the x-axis. (2 points)

Answer 1

Part (a)

She replaced x with -x to go from f(x) = 3(2)^x to g(x) = 3(2)^(-x). This will not reflect the graph of f(x) over the x axis. Instead, it will reflect over the y axis. This is because each input is negated from positive to negative, or vice versa. For instance the old input x = 2 becomes the new input -2. Applying this idea to every x input will mirror the curve over the vertical y axis.

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Part (b)

The correct equation should be g(x) = -3(2)^x

The negative out front is the same as -1.

We can think of it as g(x) = -1*f(x). The f(x) is the output value, or y value. If we multiply each y output by -1, this will flip every point over the horizontal x axis. A point like (0,3) moves to (0,-3) after doing this operation.