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Today we're going to be looking at transforming parent functions this is section two point seven and five point seven and the algebra two books you're going to need a calculator because we're going to be graphing different types of functions in this lesson we're going to start to look at what are five different common functions that you'll be transforming in this section we have the linear function goes through the origin makes a straight line that leans to the right the quadratic function is the shape of a parabola sits on the origin point it up in the air the cubic function sits on the origin right arm in the air left arm down the square root function sits on the origin leaning up to the right and kind of slide or a hill type motion and the absolute value which sits on the origin and is a v-shape when you are transforming these functions anytime you put a plus a number on the end or a minus number on the end it's going to shift your function up or down plus moves you up — moves you down so if with our first example we have y equals x plus 4 y equals x is the shape of a linear graph the plus 4 moves it up 4 in the air, so we have a line that's moved up 4 and this is what the graph of it looks like the one right below it y equals x squared plus 3 y equals x squared is the quadratic graph it's the shape of a parabola, and we're taking this one and moving it up 3, so you have a parabola that is up three units in the air try the next to see how they've been shifted and graph a picture of what they would look like for the first one on the right we have the quit graph that's the shape of a cubic where the right arm is up and the left arm is down we're shifting it down to units so put the center of it down to, and then you want to put the right arm in the air on the left arm down below it, we have the absolute value graph it's been shifted down five, so you want to put the absolute value graph which is the shape of a V move it down five and then draw your V from there if you're graphing an absolute value in your calculator you can find the absolute value bars and math sum, and they're the first entry, so you'd want to put in absolute value of x close your parentheses and then minus five to graph that horizontal shifts moving left and moving right if you have a plus number inside the parentheses or inside the square root or inside the absolute value with X you're shifting to the left if you have a minus a number inside the parenthesis inside the absolute value or inside the square root you're shifting to the right for our first example we have y equals the square root of x plus two the square root covers the X and the plus two if I was graphing this in the calculator I'd have parentheses around X plus two because it covers over the whole square root we are shifting to the left two units, so you want to draw the square root graph which is the hill shaped graph or this little slide graph, and we want to move it left to a little for the center below that...
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