Math Problem Statement

Give me points to plot for 3^x-2

Solution

To plot the function y=3x2y = 3^x - 2, you can choose some values for xx and compute the corresponding values for yy. Here are a few points to get you started:

xxy=3x2y = 3^x - 2
-2322=1921.8883^{-2} - 2 = \frac{1}{9} - 2 \approx -1.888
-1312=1321.6673^{-1} - 2 = \frac{1}{3} - 2 \approx -1.667
0302=12=13^0 - 2 = 1 - 2 = -1
1312=32=13^1 - 2 = 3 - 2 = 1
2322=92=73^2 - 2 = 9 - 2 = 7
3332=272=253^3 - 2 = 27 - 2 = 25
4342=812=793^4 - 2 = 81 - 2 = 79

These points should give you a good curve to plot.

Would you like more points or an explanation on how to plot this function?

Here are a few related questions you might find interesting:

  1. What are the general properties of exponential functions like y=3x2y = 3^x - 2?
  2. How does shifting the graph of y=3xy = 3^x affect its shape?
  3. What is the behavior of y=3x2y = 3^x - 2 as xx approaches positive or negative infinity?
  4. How do you find the horizontal asymptote of an exponential function?
  5. Can you compare the graph of y=3x2y = 3^x - 2 with y=2x2y = 2^x - 2?

Tip: To quickly plot exponential functions, pick several integer values of xx and compute the corresponding yy-values. For smoother curves, you can also use fractional xx-values.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Graphing Exponential Functions

Formulas

y = 3^x - 2

Theorems

Exponential growth
Horizontal asymptote of exponential functions

Suitable Grade Level

Grades 9-12