Day 1 Exponential Transformations

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^(x - h) + k, where a is a constant, b is the base, h is the horizontal shift, and k is the vertical shift.

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

How does a vertical translation affect the graph of an exponential function?

Back

A vertical translation shifts the graph up or down. For example, in the function f(x) = b^x + k, the graph is shifted up by k units if k is positive and down by k units if k is negative.

Front

What is a horizontal shift in the context of exponential functions?

Back

A horizontal shift moves the graph left or right. In the function f(x) = b^(x - h), the graph shifts to the right by h units if h is positive and to the left by h units if h is negative.

Front

What transformation occurs in the function f(x) = 2^(x + 3)?

Back

The function f(x) = 2^(x + 3) represents a horizontal shift of the graph 3 units to the left.

Front

What does the transformation f(x) = 3^x + 2 indicate?

Back

The transformation f(x) = 3^x + 2 indicates a vertical translation of the graph 2 units upward.

Front

How do you identify a vertical stretch in an exponential function?

Back

A vertical stretch occurs when the coefficient a in the function f(x) = a * b^x is greater than 1. This makes the graph steeper.

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient in front of an exponential function, such as f(x) = -a * b^x, reflects the graph across the x-axis.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b is a positive constant.

Front

How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x occurs at x = 0, which gives the point (0, a * b^0) = (0, a).