1. 6-2 Comparing Functions Warm Up Lesson Presentation Lesson Quiz
Holt McDougal Algebra 2
Holt Algebra 2

2. Warm Up
For each function, determine whether the graph opens upward or downward.
1. f(x) = -4x2 + 6x + 1
downward
2. f(x) = 8x2 – x - 2
upward
Write each function in slope-intercept form.
3. Y + 3x =10
y = -3x + 10
4. -6y – 12x = 24
y = -2x - 4

3. Objectives Compare properties of two functions.
Estimate and compare rates of change.

4. The graph of the exponential function y=0. 2491e0
The graph of the exponential function y=0.2491e0.0081x approximates the population growth in Baltimore, Maryland.

5. The graph of the exponential function y=0. 0023e0
The graph of the exponential function y=0.0023e0.0089x approximates the population growth in Hagerstown, Maryland. The trends can be used to predict what the population will be in the future in each city.
In this lesson you will compare the graphs of linear, quadratic and exponential functions.

6. Example 1: Comparing the Average Rates of Change of Two Functions.
George tracked the cost of gas from two separate gas stations. The table shows the cost of gas for one of the stations and the graph shows the cost of gas for the second station. Compare the average rates and explain what the difference in rate of change represents.

7. The rate of change for Gas Station A is about 3
The rate of change for Gas Station A is about 3.0. The rate of change for Gas Station B is about 2.9. The rate of change is the cost per gallon for each of the Stations. The cost is less at Gas Station B.

8. Check It Out! Example 1
John and Mike opened savings accounts on the same day. They did not deposit any money initially, but deposited each week as shown by the graph and the table. Compare the average rates of change and explain what the rates represent in this situation.

9. Example 1 continued
Mike’s average rate of change is 26. John’s average rate of change is ≈ The rate of change is the average amount of money saved per week. In this case, Mike’s rate of change is larger than John’s, so he saves about $0.43 more than John per week

10. Example 1 continued
Mike’s average rate of change is m = = 104 = John’s average rate of change is m = = 179 ≈

11. Check It Out! Example 3
Compare the end behavior of the functions
f (x) = 4x2 and g(x) = x3.

12. Check It Out! Example 3 continued
The end behavior for the graph of f(x)= 4x2: as x approaches positive infinity, f(x) approaches positive infinity. As x approaches negative infinity, f(x)approaches positive infinity. The end behavior for the graph of g(x) = x3: as x approaches positive infinity, g(x)approaches positive infinity, as x approaches negative infinity, g(x) approaches negative infinity.

13. Example 3: Comparing Exponential and Polynomial Functions.
Compare the end behavior of the functions
f(x) = -x2 and
g(x) = 4 logx.

14. Example 3 continued
The end behavior for the graph of f(x) = –x2: as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity. The end behavior for the graph of g(x) = 4log x: as x approaches positive infinity, g(x) approaches positive infinity, as x approaches 0, g(x) → approaches negative infinity.

15. Lesson Quiz: Part 2
2. f(x) = 4ex and g(x) = log x
f(x): as x → ∞, f(x) → ∞; as x→ –∞, f(x) → 0.
g(x): as x →∞, g(x) → 1; as x → 0, g(x)→ –∞.
3. Find the equation of a quadratic function that describes the data in the table.
f(x) = 3x2 -4x -10.