Evaluating Functions
Writing Functions
Drawing Graphs
Features of Graphs
Rate of Change
100
f(x) = 3x + 1
What is f(2)?
7
100
Write a function, f(x), that shows multiplying by 2.
f(x) = 2x
100
Sketch a graph of climbing a ladder at a steady speed
straight line starts at origin and increases
100
What is coordinate of the minimum?
(-4, -3)
100
How do we find rate of change?
distance divided by time
OR
change in y values divided by change in x values
200
g(x) = 7x - 4
f(x) = -9x + 2
What is g(-2)?
-18
200
Write a function, f(x), to show multiplying by 8 and adding 4
f(x) = 8x + 4
200
Sketch a graph:
I start at the top of a ladder. Climb half way down slowly and then increase my speed
Begin at top of y-axis, draw a straight line that is decreasing and then it gets steeper half way down the y-axis.
200
The shaded region is increasing, decreasing, or constant.
Decreasing Interval
200
If I travel 20 miles in 4 hours, what is my rate of change?
5
300
g(x) = 7x - 4
f(x) = -9x + 2
What is: f(1) + g(1)
-4
300
A dog collar costs $8 and each tag costs $1. Write a function using d(x).
d(x) = 8 + 1x
300
Draw a graph. I am half way from home. I run home, walk far away, stay far away, then crawl back home.
.... drawing!
300
What is the interval of this graph that shows no movement?
2<x<5
300
The population in the year 2000 in 15,000 people and 25,000 people in the year 2005.
What is the rate of change?
2000
400
g(x) = x2 + 4
f(x) = 2x - 3x
What is f(5)?
-5
400
A stuffed bear costs $17.25 and each accessory costs $3.25. Write a function using b(x)
b(x) = 17.25 + 3.25x
400
Last class we worked on "Function Intervals"
(half-sheet of white paper)
Can you answer the two questions on the back???
We will review!
400
List ALL decreasing intervals
-6<x<-4
-2<x<2
5<x<6
400
What is the rate of change between the points?
Left point:(-5, -3) Right Point:(8, -1)
2/13
OR
0.15
500
g(x) = x2 + 4
f(x) = 2x - 3x
What is f(-2) - g(3)
-11
500
Large Pizza costs $13, each topping is $2
Small Pizza costs $9, each topping is $1
What does this mean: S(3) + S(4) > L(1)
A small pizza with 3 toppings and a small pizza with 4 toppings costs more than a large pizza with 1 topping.
500
I will hand out a half-sheet of paper... can you draw one of the graphs correctly!
we will review
500
List ALL positive intervals.
-6<x<-5
-3.5<x<5.5
500
The population in 1882 was 546,123 people. In the year 1934 the population was 423,039.
What is the rate of change? What is the predicted population in 1935?
-123,084/52 = -2,367
in 1935: 420,672