Math Problem Statement

Graph the Exponential Function f(x)=1(1/5)xf(x)=1(1/5)x by plotting the Vertical Intercept and one other point. Then write the Vertical Intercept as an ordered pair.

Solution

The vertical intercept of the function f(x)=(15)xf(x) = \left(\frac{1}{5}\right)^x is at the ordered pair (0,1)(0, 1).

Another point on the graph is (1,0.2)(1, 0.2).

Do you have any questions or need further details? Here are five related questions to consider:

  1. What is the behavior of the function as xx \to \infty and xx \to -\infty?
  2. How does the base 15\frac{1}{5} affect the shape of the exponential graph?
  3. What happens to the vertical intercept if the base changes?
  4. How can you identify the asymptote of this exponential function?
  5. How would the graph change if you multiplied the function by a constant factor?

Tip: The vertical intercept of an exponential function is always at (0,a)(0, a) where aa is the coefficient in front of the base.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Graphing

Formulas

f(x) = (1/5)^x

Theorems

Exponential Decay

Suitable Grade Level

Grades 9-12