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?
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 7. 9 5 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:
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
8. Draw your own linear that has a y-intercept of 5. 9. 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()?
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 5 9.. 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 -7-5 - domain: 8 6 - -8-6 - - 6 8 - - -6-8 - graph below. y Range: