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Overview
ALEKS Exponentials and Trigonometry
Exponential functions
2. Graphing exponential functions
2.3 Exponential function graph
Exponential Function Graph
See exactly how to graph an exponential function, from the parent curve to growth, decay, and transformations, with step-by-step examples.
What You'll Learn
An exponential function has the form \(y = b^x\), where the variable is in the exponent rather than the base.
When \(b > 1\) the graph shows exponential growth, and when \(0 < b < 1\) it shows exponential decay.
Every basic exponential graph has a horizontal asymptote at \(y = 0\), a y-intercept at \((0, 1)\), and never touches the x-axis.
Transformations shift, stretch, reflect, or flip the parent graph, moving the asymptote and intercept accordingly.
Exponential graphs eventually grow or shrink much faster than linear or quadratic graphs.
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Learning resources
TEST-PREP Curriculum Aligned