3A and 3B Interpreting Functions
f(4) means to substitute (4) into the equation for x and evaluate. It also means that x=4
Ex: f(x) = 2x + 3 f(4) 2(4) + 3 11g(x) = 2x2 – x + 4. Find g(1) 2(1)2 – 1 + 4 2-1+45
f(a + 2) means to substitute (a+2) into the equation for x and simplify.
Ex: f(x) = 2x + 3 f(a+2) 2(a + 2) + 3 2a + 4 + 3 2a + 7
f(x) = 4 means that the equation is = 4 and solve for x. It also means that y=4
Ex: f(x) = 2x + 3 f(x) = 4 2x + 3 = 4 2x = 1 x = ½
The cost of a taxi ride is given the equation C(m) = 5m + 2.
Find C(3) and interpret 5(3)+217. Cost is $17 after 3 miles
Find C(m)=22 & interpret 5m+2=22 5m=20m=44miles=$22
Using a graph; f(3) means that x = 3, find the y-coordinate
f(x) = 3 means that y=3, find the x-coordinate
y-intercept: Where the graph crosses the y-axis and x=0 <f(0)>
x-intercept: Where the graph crosses the x-axis and the y=0 <f(x)=0>
Increasing: Where the graph is going up (left to right). Give x-values.
Decreasing: Where the graph is going down (left to right). Give y-values.
f(2) After 2 minutes (x value) , Sally is on the 4th floor (y value).
f(x) Sally is on the first floor (y value) after 5 ½ minutes(x –value)
y-intercept: f(0): Sally is on the 2nd floor at 0 minutes
x-intercept: Sally is on the 0 floor after 6 minutes.
Increasing: 0 x 2 Decreasing: 4x6
Function: If the x-values do not repeat then it is a function
Ex: {(0,1), (2,3), and (3,1)} is a function; {(2,3),(3,4),(2,5)} isn’t a function. The above is a function
Example: Is (2, 5) a solution to 3x + 2y = 16?
Substitute the ordered pair into the equation. 3(2)+2(5)= 6+10 16=16 ✓
Practice
For 1-8 use the following equations: f(x) = 2 – 4xg(x) = 2x2 – 5x + 3
1)Find f(3)2) Find f(-2)3) Find f(a + 3)4) Find f(x) = 0
5) Find y-intercept of f(x)6) Find g(-2)7) Find g(1)8) Find y-intercept of g(x)
9-10). The cost of yogurt is given by the equation C(w)=.25w + 1.00 where w is the weight in ounces.
9) Find and interpret C(8)10) Find and interpret C(w) = 5
11-12) The number of flowers in a garden is given the by equation F(d) = 3d + 5 where d is number of days.
11) Find and interpret F(5). 12) Find and interpret F(d) = 35.
Use the following graph for problems 13-20
13) Find and interpret the y-intercept
14) Find and interpret the x-intercept
15) Find and interpret f(2)
16) Find and interpret f(x) = 1
17) Find and interpret f(1)
18) Where is the graph increasing?19) Where is the graph decreasing20) Is it a function?
21) Is {(2,3), (7,1), (2,3)} a function?22) Is {(2,4), (5,6), (8,6)} a function?
23) Is (2, -3) a solution to ? 24) Is (-5, 2) a solution to ?
25) After what value of x does exceed ?
26) After what value of x does exceed ?
Determine which of the following are functions.
27) {(6, 3), (7, 2), (0, 2)} 28) 29)
30)31) 32) 33)
34)35)36)37)