Find the exponential function f(x)=ax whose graph is given. Function pass point (0,1) and (-2, 1/16). #1. Find the exponential function \( f(x) = a^x \) whose graph is given. The function passes through the points \( (0, 1) \) and \( \left(-2, \frac{1}{16}\right) \).### Graph DescriptionThe graph shows an exponential curve. It crosses the y-axis at the point \( (0, 1) \), indicating that when \( x = 0 \), \( f(x) = 1 \). This point suggests that the base \( a \) raised to the power of 0 is equal to 1, which is true for any non-zero value of \( a \).Another indicated point on the graph is \( \left(-2, \frac{1}{16}\right) \). This point helps determine the base \( a \) of the exponential function. The curve exhibits growth as it moves from left to right, which is characteristic of exponential functions with bases greater than 1.### Steps to Find the Base \( a \)1. Use the point \( (0, 1) \) to establish that \( a^0 = 1 \), confirming that \( a \) is valid.2. Use the point \( \left(-2, \frac{1}{16}\right) \): \[ f(-2) = a^{-2} = \frac{1}{16} \] This equation can be solved to find \( a \): \[ a^2 = 16 \quad \Rightarrow \quad a = \sqrt{16} = 4 \]Thus, the exponential function is \( f(x) = 4^x \).

Given: f(x) = ax At x=0, f(x) = 1 and for x=-2, f(x)=116 Now, substituting the value of x=-2, we get 116=a-2 116=1a2 142=1a2 On comparison , we get a=4 Thus, the function will be f(x)=4x

Answered: #1. Find the exponential function f(x)…

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#1. Find the exponential function f(x) = a* whose graph is given. Function pass point (0, 1) and (-2, →)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Find the exponential function f(x)=a^x whose graph is given. Function pass point (0,1) and (-2, 1/16).

#1. Find the exponential function \( f(x) = a^x \) whose graph is given. The function passes through the points \( (0, 1) \) and \( \left(-2, \frac{1}{16}\right) \).

### Graph Description
The graph shows an exponential curve. It crosses the y-axis at the point \( (0, 1) \), indicating that when \( x = 0 \), \( f(x) = 1 \). This point suggests that the base \( a \) raised to the power of 0 is equal to 1, which is true for any non-zero value of \( a \).

Another indicated point on the graph is \( \left(-2, \frac{1}{16}\right) \). This point helps determine the base \( a \) of the exponential function. The curve exhibits growth as it moves from left to right, which is characteristic of exponential functions with bases greater than 1.

### Steps to Find the Base \( a \)
1. Use the point \( (0, 1) \) to establish that \( a^0 = 1 \), confirming that \( a \) is valid.
2. Use the point \( \left(-2, \frac{1}{16}\right) \):
\[
f(-2) = a^{-2} = \frac{1}{16}
\]
This equation can be solved to find \( a \):
\[
a^2 = 16 \quad \Rightarrow \quad a = \sqrt{16} = 4
\]

Thus, the exponential function is \( f(x) = 4^x \).

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