Math Problem Statement

draw the graph of f(x)=3^x+2

Solution

Here is the graph of the function f(x)=3x+2f(x) = 3^x + 2. The curve shows an exponential growth, shifted upward by 2 units due to the "+2" term.

Would you like more details or have any questions about the graph or the function?

Here are 5 related questions to deepen your understanding:

  1. How would the graph change if the function was f(x)=3x2f(x) = 3^x - 2?
  2. What is the behavior of f(x)=3x+2f(x) = 3^x + 2 as xx \to \infty and xx \to -\infty?
  3. Can you find the y-intercept of the function f(x)=3x+2f(x) = 3^x + 2?
  4. What happens to the graph if you change the base from 3 to another number, like 2 or 5?
  5. How would you solve the equation 3x+2=y3^x + 2 = y for xx?

Tip: For exponential functions, the base of the exponent determines the growth rate. The higher the base, the faster the function grows.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Transformations

Formulas

f(x) = a^x + k (Exponential function with vertical shift)

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 9-11