Math Problem Statement
The y-intercept of the exponential function y=6^x is 1.
Solution
The y-intercept of any function is the value of when . Let's verify this for the exponential function :
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Substitute into the function:
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Using the property of exponents (where ):
Thus, the y-intercept of is indeed .
Would you like more details or have any questions?
Here are 5 related questions to explore further:
- What is the slope of the tangent line to at ?
- How does the base of the exponential function affect its y-intercept?
- What are the asymptotes of the function ?
- How does the graph of compare to ?
- If the function were , how would the y-intercept change?
Tip: The base of an exponential function always determines how steeply the graph grows or decays as increases or decreases.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Properties of Exponents
Graph Intercepts
Formulas
y = a^x
a^0 = 1
Theorems
Exponentiation Rules
Suitable Grade Level
Grades 9-10