f x f x f x f x x 5 3 y-intercept: y-intercept: y-intercept: y-intercept: y-intercept of a linear function written in function notation

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1 Questions/ Main Ideas: Algebra Notes TOPIC: Function Translations and y-intercepts Name: Period: Date: What is the y-intercept of a graph? The four s given below are written in notation. For each one, fill in the table of values, then graph assuming they are continuous. -What does continuous mean? THEN, state the y intercept -What is the y-intercept? f f f f f f f f 5 What is a coefficient? _ SIMILARITIES DIFFERENCES What do all the rules have in common? What is different among all rules? What do all the graphs have in common? What is different among all graphs? y-intercept of a linear written in notation How does the rule define the y-intercept? f Number after term: y-intercept: f Number after term: y-intercept: f Number after term: y-intercept: f Number after term: y-intercept: Do you see a pattern?

2 Rules of notation CONCLUSIONS (only for s written ): Two linear s written in notation that have the same coefficient of must always: The number in the rule that does not have an You try. f 5. f. f f 5. Which s in problems above would you epect to have the same shape? Why? Let s apply the rules we just learned to other s that are not linear. Below are graphs of s f, g, and h. Use the same y-intercept rule you just learned to draw the graph requested in each case. Draw f Draw g Draw h f g h So, for s written in, we can say: Adding a number to the will: What is a translation? Subtracting a number from the will: This shifting of the across the coordinate plane is called. Summary:

3 Algebra Guided Practice Translations and y-intercept Name Block Date. f. f. f 6. f 5 5. Which s in problems through above would you epect to have the same shape? Why? Match each on the left to its appropriate graph on the right. 6. f A. B. C. 7. f 8. f 9. f. f 5 D. E. F.. f 5. Given g below,. Given h below,. Given f draw g draw h 5 draw f below, 5. Write the epression for the g translated seven units up 6. Write the epression for the f translated eight unit down 7. Write the epression for the h translated half a unit up

4 8. Draw your own linear that has a y-intercept of Shift your original down 6 units. What is the new y-intercept?. Draw a new linear that has a y-intercept of and label it f(). Shift f() up units and label the new graph g(). Shift g() down 6 units and label the new graph h(). What is the y-intercept of f()? What is the y-intercept of g()? What is the y-intercept of h()?

5 Algebra Independent Practice Translations and y-intercept Name Block Date. f 7. f 8. f 7. f 7 5. Which s in problems through above would you epect to have the same shape? Why? Match each on the left to its appropriate graph on the right. 6. f A. B. C. 7. f 8. f f 5 f D. E. F.. f. Look at the graphs in A-F, which are decreasing? Look at the s that correspond to the decreasing graphs, what do you notice?. Look at the graphs in A-F, which are increasing? Look at the s that correspond to the increasing graphs, what do you notice?. Do you think that increasing and decreasing is connected to the slope of the? Why or why not? 5) Given 6 f, complete the table. 6) Create a table of values from the Then plot the and fill in the blanks. y domain: graph below. y Range:

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such.

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Review Exercise Set 13 Exercise 1: Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Exercise 2: Write a linear function that can