Evaluate the function f(x) = 4x + 6 for x = 4
f(x) = (4*4) + 6
f(x) = 22
Evaluate the function f(x) = 9x - 6 for x=0.
f(x) = (9*0) – 6
f(x) = -6
a) Equation for f(x), assuming the function is linear.
When x = -2, f(x) = -5; and when x = 2, f(x) = 7
f(x) = a + bx, “a” is a constant.
“b” is the gradient or slope of the line.
a = 1. This is because when “x” is zero, 0, “f(x)” is equal to the constant value, which is 1
f(x) = 1 + 3x
b) The slope is 3, which is positive.
The information we get from the slope is that, the relationship between “f(x)” and “x” is positive, and that an increase in “x” by one will result in an increase in “f(x)” by 3.
Suppose you have a cookie stand, when you charge $3 per cookie box you sell 200 boxes, but when you charge $4 per cookie box, you only sell 120 boxes.
"B" denotes the number of boxes, and "P" denotes the price you charge. Assuming the function is linear, the equation for the number of boxes you sell as a function of the price you charge, is as follows.
When P = $3, B = 200; and when P = $4, B = 120.
B = f(P) = mP + a
a= B – mP = 200 – (-80*3) = 200 + 240 = 440
B = 440 – 80P
A reservation clerk worked 12.6 hours one day. The time she spent entering new reservations was twice as much time as she did verifying old ones, and one and a half as much time calling to confirm reservations as verifying old ones.
The calculation of the time spent entering new reservations is as follows.
Let “X” denote the number of hours used to enter new reservations.
Let “Y” denote the number of hours used to verify old reservations.
Let “Z” denote the number of hours used to confrim reservations.
X = 2Y, and Z = 1.5Y
2Y + Y + 1.5Y = 12.6 hours
4.5Y = 12.6 hours
X = 2Y = (2*2.8 hours)
X = 5.6 hours.
Therefore, she spent 5.6 hours entering new reservations.
4. Differentiate between a function and a linear function.
A function is a mathematical rule that shows that one quantity, that is, an input, determines another quantity, which is the output.
A linear function is a type of a function, whose graph is a straight line. It is a first-degree function, that is, each variable in the function is raised to the first power. It has a one slope or gradient, and a constant value, which is the y-intercept. The mathematical equation of a standard linear function is f(x) = mx + b, where “m” is the gradient and “b” is the constant or y-intercept.