Writing Exponential Functions from a Graph and Table

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the value of the function when x=0. It represents the starting point of the graph.

Front

How do you find the ratio in an exponential function?

Back

The ratio is the constant factor by which the function's output changes as x increases by 1. It can be found by dividing the output values of consecutive x values.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the y-intercept and 'b' is the base or ratio.

Front

How do you write an exponential function from a table of values?

Back

Identify the y-intercept (value when x=0) and the ratio (how y changes as x increases). Use these to form the equation f(x) = a * b^x.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor of the function. If b > 1, the function grows; if 0 < b < 1, it decays.

Front

What is an example of an exponential function with a base of 2 and a y-intercept of 5?

Back

f(x) = 5 * 2^x.

Front

How can you determine if a function is exponential from a graph?

Back

An exponential function will show a rapid increase or decrease and will have a characteristic curve that is not linear.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept indicates the initial value of the function before any growth or decay occurs.

Front

How do you identify the base of an exponential function from a graph?

Back

The base can be determined by observing how much the function's output increases for each unit increase in x.

Front

What is the exponential function for a y-intercept of 10 and a ratio of 1/2?

Back

f(x) = 10 * (1/2)^x.