Math Problem Statement

Graph the given function by making a table of coordinates. f left parenthesis x right parenthesis equals 5 Superscript x Question content area bottom Part 1 Complete the table of coordinates. x minus2 minus1 0 1 2 y    enter your response here    enter your response here    enter your response here    enter your response here    enter your response here ​(Type integers or fractions. Simplify your​ answers.)

Solution

To graph the given function f(x)=5xf(x) = 5^x, we calculate the yy-values for each given xx-value using the formula y=5xy = 5^x.

Calculations:

  1. x=−2x = -2: y=5−2=152=125y = 5^{-2} = \frac{1}{5^2} = \frac{1}{25}

  2. x=−1x = -1: y=5−1=15y = 5^{-1} = \frac{1}{5}

  3. x=0x = 0: y=50=1y = 5^0 = 1

  4. x=1x = 1: y=51=5y = 5^1 = 5

  5. x=2x = 2: y=52=25y = 5^2 = 25

Completed Table:

\hline x & y = 5^x \\ \hline -2 & \frac{1}{25} \\ -1 & \frac{1}{5} \\ 0 & 1 \\ 1 & 5 \\ 2 & 25 \\ \hline \end{array}$$ If you'd like, I can also plot the graph for you. Let me know! --- Do you want more details or any additional help? ### 5 Related Questions: 1. What happens to the graph of $$f(x) = 5^x$$ when $$x$$ approaches infinity? 2. How does $$f(x) = 5^x$$ compare to $$f(x) = 2^x$$? 3. How do negative exponents affect the values of exponential functions? 4. What are the key properties of exponential functions like $$5^x$$? 5. How would the graph change for $$f(x) = 5^{-x}$$? ### Tip: Always check the values of exponential functions at $$x = 0$$ and nearby integers to understand their growth or decay behavior.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Coordinate Graphing
Negative and Positive Exponents

Formulas

y = a^x
y = 5^x

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-11

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