Exercise 1 and 2
1) Sales tax is a function of the price of an item. The amount of sales tax is 0.08 times the price of the item
The independent variable, x, is price of an item.
The dependent variable, f (x), is sales tax.
Equation: f (x) = 0.08 * x
2) The Fahrenheit measure of temperature is a function of the Celsius measure . The Fahrenheit measure is 32 more than
times the Celsius measure
The independent variable, x, is Celsius measure of temperature.
The dependent variable, f (x), is Fahrenheit measure of temperature.
Equation: f (x) = 32 +
* x
Exercise 3, 4 and 5
3) f (d) = 2d - 5 = 2×d - 5
f (2) = 2×2 - 5 = 4 - 5 = -1
f (-3.2) = 2 × (-3.2) - 5 = -11.4
f (a) = 2×a - 5
4) f (t) = -16t² + 7.8t + 12 = -16 × t² + 7.8 × t + 12
f (2) = -16 × 2² + 7.8 × 2 + 12 = -64 + 15.6 + 12 = -36.4
f (-3.2) = -16 × -3.2² + 7.8 × -3.2 + 12 = -163.84 - 24.96 + 12 = -176.8
f (a) = -16 × a² + 7.8 × a + 12
5) f (x) = 4
f (2) = 4, since f (x) is not dependent on x, its value will always be constant
f (-3.2) = 4
f (a) = 4
6) We need to construct a table with 4 unique values of x (starting at 0 and with increment of 5) and corresponding values of f(x)
f (x) = 3.5x + 6 = 3.5*x + 6
For x = 0, 5, 10 and 15, we need to find values of f(x)
f (0) = 6
f (5) = 3.5*5 + 6 = 17.5 + 6 = 23.5
f (10) = 3.5*10 + 6 = 35 + 6 = 41
f (15) = 3.5*15 + 6 = 52.5 + 6 = 58.5
See attachment for the table