2 2 Linear Relations Functions Any linear functions

2. 2 Linear Relations & Functions

Any linear functions can be written as f(x) = mx + b, where m and b are real numbers. This means, to be linear… *degree of input variable must be one *two or more variables cannot be multiplied *input variable can never be in denominator

Example 1: a) State whether the following are linear functions. Explain your reasoning. A) B) g(x, y) = 3 xy C) p(x) = x 3 + 2 D) E) f(x) = x 2 – 4 F) t(x) = 4 + 7 x

Evaluating a Linear Function Example 2: The function f(C) = 1. 8 C + 32 can be used to find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C. Normal body temperature is 37 C. What is it in degrees Fahrenheit?

Create a Linear Function and solve! Example 3: You want to make sure you have enough music for a long car trip. Each CD is an average of 45 min. and you also plan on listening to the radio for 60 min. – Create a linear function that represents how many CD’s (x) you need to bring for h hours in the car – If you listen to 5 CD’s, how long was the trip? – How many CD’s would you listen to on a 16 hour road trip?

Linear Functions in Standard Form Ax + By = C • A, B and C are integers • A≥ 0 When finding an x or y intercept, set the opposite variable and equal it to zero b/c… • x-intercept: (x, 0) y = 0 • y-intercept: (0, y) x = 0

Example 4: Find the x-intercept and y-intercept of the graph -2 x + y – 4 = 0. Example 5: Write the equation of the graph in standard form with intercepts at (2, 0) and (0, 6).