Graph each function. See Examples 6–8. _ƒ(x) = 2√x + 1

Question

Accepted Answer

Hello, everyone. We are asked to draw the graph of the following function. We are given F of X equals five, multiplied by the square root of X plus four. We were given a Cartesian plane with a scale of one with marked interval on the X axis from negative 15 to positive 15 and on the Y axis from negative to positive 15. First, I want to identify what my parent function is for this graph. So our parent function is what is our base function if there were no stretches, shifts or anything like that. And since we have F of X equals five multiplied by the square root of X plus four, I'm gonna say our parent function is the function the square it of X. So G of X is the squared of X. That is our basic function. Recall that that starts at the origin and is a curve in the first quadrant. So now using that base parent function, I'm gonna look at F of X equals five multiplied by the squared of X plus four. The first thing I notice is the plus four, this means that the starting point is going to shift up four units. So we're no longer gonna start at 00, we're gonna start at the 0.04. So I put that on my graph next, the number in front of the square root of X tells me that this will be stretched. So instead of just being a small curve, it's gonna be a much larger curve. And so it's gonna be stretched vertically by a factor of five. So since we're not using exact points, I'm gonna kind of rough hand this a little bit. So it's gonna be a curve and it looks like it will go out of my plane even, but it looks like it crosses at 5 15. So we have an angle in the first quadrant. It's a curve and it ends up outside of our quadrant even if I wanted to keep drawing, but it is stretched by a factor of five and its starting point is shifted up. Four units have a nice day.

Graph each function. See Examples 6–8. _ƒ(x) = 2√x + 1

Key Concepts

Square Root Function

Transformation of Functions

Domain and Range

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