UNIT #2 TRANSFORMATIONS OF FUNCTIONS

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1 Name: Date: UNIT # TRANSFORMATIONS OF FUNCTIONS Part I Questions. The quadratic unction ollowing does,, () has a turning point at have a turning point? 7, 3, 5 5, 8. I g 7 3, then at which o the The structure o this transormation indicates that the graph o has been shited let 7 units due to 7 being added to the input. And then the graph has been shited down 3 units due to 3 being subtracted rom the unction. Hence:. Where does the absolute value unction 4, 3 8, 3 y 8 3 have a turning point? This unction is a shit o 8 right and 3 up o the more simple unction, which has a turning () 4, 3 8, 3 point at. Thus, it will have a turning point at 3. The unction is shown below graphed in solid while the unction ollowing equations describes the relationship between the two unctions? g is shown dashed. Which o the g 6 () g g g g The graph o has been both relected and compressed vertically to produce the graph o. To do this, one has to multiple the entire unction by a negative number between 0 and -. () 4. Given that the unction 6 7 has -intercepts at 9 and 3, where does the unction y y have -intercepts? 6 7 and 9 () and 0 3 and Since is an -intercept o this unction we know: But, this allows us to simply solve the ollowing.

2 5. I the point 3, 7 y 5 0? lies on the graph o, then which o the ollowing points must lie on the graph o, 3 5, 3 3,5 (), 5 () 6. The range o the unction or g? is 4 y 0 7 y 7 3 y () 5 5 y g. I 3 3 y 8 The structure o a relection o then which o the ollowing is the range indicates that its graph is in the -ais ollowed by an upward shit o 3 units. Thus, the range would be transormed as: 7. The trinomial can be written equivalently as () 0 45 Multiply each o the ollowing pairs o binomials to see which is equivalent to the original trinomial. Choice gives: 8. The cubic polynomial can be actored as () () 9. The equation has a solution set o 5,, 7 3, 0, 7 3 () 5,, 7, 0, 7

3 0. The quadratic unction its other zero? has one zero at 6 3. At which o the ollowing -values is Since is a zero, then must be a actor o this polynomial. But, this means it must actor as: () 5 4 Which means its other zero must be (). The parabola y can be written in the orm y y 3 3 () y y Free Response 3. For the unction it is known that, 4 lies on the unction. A second unction, the ormula g 3. Describe the transormations that occur to the graph o in order to produce the graph o g. Based on the act that the point There are two transormations that occur:. A horizontal compression by a actor o (or i you preer a actor o /). A vertical shit by 3 units downward., 4 lies on, what point must lie on g? g, is deinedby Note that we can veriy our answer by evaluating :

4 4. The graph o the unction g or all values o. is shown below. The unction is deined by the ormula Produce the graph o g on the same grid. Solve the equation g or all values o. To solve any equation graphically, simply ind the -values where the outputs (y-values) are the same. In other words, give the -values o the intersection points: g. 5. The graph o is shown below. The unction g is deined by 5 Eplain the transormations that will transorm the graph o g and then into the graph o produce it on the same grid. Two transormations have occurred to in order to produce the graph o g. These can occur in either order:. A horizontal stretch by a actor o.. A vertical stretch by a actor o Given the parabola y into the graph o 8 5, describe three transormations which would transorm the graph o. Give both the transormations and the order. There are multiple orders o transormations. We will present two correct options. Option #:. A horizontal shit right by 8 units.. A relection in the -ais. 3. A vertical shit upwards o 5 units. Option #:. A relection in the -ais.. A horizontal shit right by 8 units. 3. A vertical shit upwards o 5 units.

5 7. Describe the dierence between the transormations and on the graph o. The transormation will relect the The transormation will relect the graph o in the y-ais. graph o in the -ais. 8. Factor the epression below completely Shana believes one o the two binomial actors o 35 8 is 3. Is she correct? Eplain your answer. The second actor would have to be in order or the quadratic term o and the constant term o 8 match. Although, the quadratic and constant terms match, the linear term o does not match the correct term o. 0. Find each o the ollowing cube roots without the use o your calculator. Justiy your answer based on a multiplication statement. (a) 3 8 (b) 3 (c) 3 5 (d) 3 0 (e) 3 8 () 3 7 (g) 3 64 (h) 3 000