Question

How does changing the number outside the parentheses of an exponential function change your graph? y = a(b)^x

Answer 1

Answer:

See Below.

Step-by-step explanation:

We have the function:

$y=a(b)^x$

Depending on the behavior of the coefficient, many things can happen. The parent exponential function has a=1. If a is something other than 1, however, there are three main changes.

Let’s use b=2 to illustrated the examples.

(In the graphed examples, below, the parent function (with b=2) is the red curve.)

• If a is a positive, rational number greater than 1.

If a is a positive number other than 1, say 2, then this represents a vertical stretch.

In other words, our function is stretched closer to the y-axis.

(This is the blue curve. It is closer to the y-axis than the parent function (red curve).)

• If a is a positive, rational number greater than 0 but less than 1.

If a is a number between 0 and 1 (so a fraction), say, 1/2, then this represents vertical compression.

In other words, our function gets farther away from the y-axis.

(This is the black curve.)

• If a is a negative.

If a is negative, then this means that the graph was flipped over the x-axis.

(This is the green curve.)

Note that if we have something such as a=-2 or a=-1/2, this means that the function we flipped over the x-axis first and then vertically stretched or compressed.

(And example of this is illustrated with the orange curve).