Lesson 4
Interpreting Functions
- Let’s interpret some functions.
4.1: Math Talk: Finding Outputs
Mentally evaluate the output for the input of 3.
\(f(x) = 4\left( x - \frac{1}{2}\right)\)
\(g(x) = 2(6 - x)\)
\(h(x) = \frac{5}{3}x + \frac{1}{3}\)
\(j(x) = 0.2x - 1\)
4.2: It’s Getting Hotter
![an antique Grohe temperature gauge](https://cms-im.s3.amazonaws.com/5nohcLjAJMvfh1Yr7dbtZAYC?response-content-disposition=inline%3B%20filename%3D%22Grohe%20thermostat.jpg%22%3B%20filename%2A%3DUTF-8%27%27Grohe%2520thermostat.jpg&response-content-type=image%2Fjpeg&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005326Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8f8b0ea4451b3811df38fb644f56b8d102c421564e75e2e35d4b8bc1fbcb8465)
A machine in a laboratory is set to steadily increase the temperature inside. The temperature in degrees Celsius inside the machine after being turned on is a function of time, in seconds, given by the equation \(f(t) = 22 + 1.3t\).
- What does \(f(3)\) mean in this situation?
- Find the value of \(f(3)\) and interpret that value.
- What does the equation \(f(t) = 35\) mean in this situation?
- Solve the equation to find the value of \(t\) for the previous question.
- Write an equation involving \(f\) that represents each of these situations:
- The temperature in the machine 30 seconds after it is turned on.
- The time when the temperature inside the machine is 100 degrees Celsius.
4.3: You Charge How Much?
- Which line represents \(y = f(t)\)? Explain how you know.
- The lines intersect at the point \((4,900)\). What does this point mean in this situation?
- Which is greater, \(f(10)\) or \(g(10)\)? What does that mean in this situation?
- Your group has $1,500 to spend on supercomputer time. Which company should your group use?
- Explain or show your reasoning using the equations.
- Explain or show your reasoning using the graph.