Question

Consider the relationship 3r - 4t = 9. a. Write the relationship as a function r=f(t). Enter the exact answer. f(t) = ____. b. Evaluate f(−3). f(−3) = ____. c. Solve f(t) = 11. t = ____.

Answer 1

The relationship as a function of t is f(t) = (4/3)t + 3. When evaluating f(−3), the result is -1. To solve for f(t) = 11, the value of t is 6.

Step-by-step explanation:

To write the relationship 3r - 4t = 9 as a function r=f(t), solve for r:

• 3r = 4t + 9
• r = (4t + 9)/3
• f(t) = (4/3)t + 3

Part b: To evaluate f(−3), substitute -3 for t in the function:

• f(−3) = (4/3)(−3) + 3
• f(−3) = −4 + 3
• f(−3) = −1

Part c: To solve f(t) = 11, set the function equal to 11 and solve for t:

• (4/3)t + 3 = 11
• (4/3)t = 8
• t = 8 / (4/3)
• t = 6