QuestionWhich graph shows the function $g(x)=-\sqrt{x+3}$ ? Explain the effects of the negative sign and the square root.

Studdy Solution

STEP 1

Assumptions1. We are dealing with the function $g(x)=-\sqrt{x+3}$ . We need to understand the behavior of the square root function and the effect of the negative sign before the square root3. We are dealing with real numbers only

STEP 2

Let's start by understanding the basic square root function, $f(x) = \sqrt{x}$ . This function is defined for $x \geq0$ and the graph of this function starts from the origin (0,0) and increases as x increases. It is a half parabola lying on the right side of the y-axis.

STEP 3

Now, let's consider the function $h(x) = \sqrt{x+3}$ . This is a horizontal shift of the basic square root function $f(x) = \sqrt{x}$ . The "+3" inside the square root shifts the graph3 units to the left. So, the graph of $h(x)$ starts from the point (-3,0) and increases as x increases.

STEP 4

Finally, let's consider the function $g(x) = -\sqrt{x+3}$ . The negative sign before the square root reflects the graph of $h(x) = \sqrt{x+3}$ about the x-axis. So, the graph of $g(x)$ starts from the point (-3,0) and decreases as x increases.

STEP 5

In conclusion, the graph of the function $g(x)=-\sqrt{x+3}$ is a reflection of the graph of the basic square root function $f(x) = \sqrt{x}$ about the x-axis, and shifted3 units to the left. It starts from the point (-3,0) and decreases as x increases.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms