Graphing Exponential Functions
Graph exponential functions in Grade 10 algebra. Identify base, initial value, and growth or decay factor, plot key points, and describe transformations of y=a·bˣ on coordinate axes.
Key Concepts
New Concept A function of the form $y = ab^x$ is an exponential function if $x$ is a real number, $a \neq 0$, $b 0$, and $b \neq 1$.
What’s next Next, you’ll explore the parent function $y=b^x$ by creating tables and graphing curves to see how these powerful functions behave.
Common Questions
What are the key features of an exponential function graph?
Exponential functions y = a·bˣ have a y-intercept at (0, a), a horizontal asymptote at y = 0, and pass through (1, a·b). For b > 1 the graph grows, for 0 < b < 1 it decays.
How do you plot an exponential function step by step?
Identify a (initial value) and b (base). Plot y-intercept at (0, a). Calculate a few more points by substituting x = 1, 2, -1. Draw the smooth curve approaching the horizontal asymptote.
How do you distinguish exponential growth from exponential decay?
Exponential growth has b > 1 (e.g., b = 2): the graph rises steeply to the right. Exponential decay has 0 < b < 1 (e.g., b = 0.5): the graph falls and approaches y = 0.