The table in the image requires identifying the type and behavior of given functions as either linear or exponential. Here's how to determine the type and behavior for each function:

Types of Functions:

1. Linear Functions are in the form $y = mx + b$, where $m$ and $b$ are constants.
2. Exponential Functions are in the form $y = a \cdot b^x$, where $a$ is a constant and $b$ is the base of the exponential.

Behavior of Functions:

• Linear Growth/Decay: Linear functions have a constant rate of change (slope).
  • Positive slope $m > 0$: Linear Growth.
  • Negative slope $m < 0$: Linear Decay.
• Exponential Growth/Decay: Exponential functions have a rate of change proportional to their value.
  • Base $b > 1$: Exponential Growth.
  • Base $0 < b < 1$: Exponential Decay.

Analyzing Each Function:

1. $f(x) = 45x - 80$

   • Type: Linear (since it's in the form $mx + b$)
   • Behavior: Growth (since the slope $45 > 0$)

2. $d(y) = 8(4)^y$

   • Type: Exponential (since it's in the form $a \cdot b^x$)
   • Behavior: Growth (since the base $4 > 1$)

3. $p(t) = 190(1.2)^t$

   • Type: Exponential
   • Behavior: Growth (since the base $1.2 > 1$)

4. $g(x) = -18x + 250$

   • Type: Linear
   • Behavior: Decay (since the slope $-18 < 0$)

5. $h(x) = 200(0.9)^x$

   • Type: Exponential
   • Behavior: Decay (since the base $0.9 < 1$)

Summary Table:

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

Related Questions:

1. How do you identify the slope in a linear function?
2. What are some real-world examples of exponential growth and decay?
3. How do you determine the y-intercept of a linear function?
4. What is the difference between exponential growth and linear growth?
5. Can an exponential function have a negative base?

Tip:

When analyzing functions, always look for the form of the equation first; it helps in identifying the type and behavior.