Function Notation & Direct Variation
Date:
Function Notation:
The equation y = 3x means that y is a “function” of x
 y = f(x)
 Can be written as f(x) = 3x
 This is “f of x” (not f times x)
 The f can be replaced with any letter such as h(x), g(x), etc.
Functions take one value from the domain(x values) and assigns it to a value in the range(y values)
Examples:
1. If f(x) = 4x – 2, evaluate f(1)
a. Substitute 1 in for x in the equation and solve for f(x)
f(x) = 4x – 2
= 4(1) – 2
= 4–2
= 2
2. Evaluate g(-2), if g(x) =
1
x +2
2
3. Evaluate the given function for f(3), if f(x) = x2 – 5x.
4. If h(x) = -x + 3 and h(x) = 12, what is the value of x?
a. Set the two functions equal to each other and solve for x
*** On graphing calculator ***
Y1 = -x + 3
Y2 = 12
2nd Calc intersect
Check window – Move to y max = 20
Intersect point is the answer
Direct Variation
Direct variation occurs when y = mx+ b,
 b = 0 (line passes through origin)
 m≠0
 Becomes y = mx
 m(or slope) is the constant of variation
 So we now have y = kx (recall k was constant of variation in chapter 6)
y
 Solving for k, we get k =
x
Examples:
Solve for y
y = 7x
1. y = 7x
Is the equation in
the form y = kx?
Yes
Is it a direct
variation?
Yes
Constant of
Variation
7
2. y = 4x – 10
3. 5x – 2y = 0
Complete the table:
y
for
x
each ordered pair
Find the value of
x
y
10
2
15
3
20
4
x
y
4
16
8
20
12
24
y
the same
x
for each ordered pair?
Is the value of
Direct Variation?
Word Problems
 Set up as a proportion
1. The number of miles driven varies directly with the number of gallons of gas used. Erin drove 297
miles on 9 gallons of gas. How far would she be able to drive on 14 gallons of gas?
2. The number of people that can be seated in a lecture hall varies directly with the number of rows of
seats. If 72 people can be seated in 4 rows, how many people can be seating in 13 rows?
Homework: pg. 228 1 & 2 (a, e, g only), 3, 4, 5
pg. 230 1a, b, c, d, 2, 4, 7 – 13 odds