We are asked to match the graph of a square root function with its equation. Let's look at the given graph. We will call the function on the graph f(x).
Now, let's look at the given options.
Option
Equation
A
y=-2sqrt(x)+1
B
y=-2sqrt(x)+3
C
y=2sqrt(x)+3
D
y=2sqrt(x)+1
We can see that all of the given equations are transformations of the same parent function, y= 2sqrt(x). Therefore, we know that f(x) is also a transformation of y= 2sqrt(x). Let's compare the given function f(x) with the parent function.
The parent function y= 2sqrt(x) increases as x increases while f(x) decreases as x increases. If we reflect the parent function in the x-axis, both f(x) and the reflected parent function will decrease as x increases. The reflection of the parent function y= 2sqrt(x) in the x-axis is the function y= -2sqrt(x)
Now, notice that the y-intercept of the function f(x) is 3 and the y-intercept of the function y= -2sqrt(x) is 0.
Therefore, function f(x) must be a translation 3 units up of the function y= -2sqrt(x). We can write this algebraically as f(x)= -2sqrt(x)+ 3.
Finally, we can write the graphed function f(x) as an equation by exchanging f(x) with y.
f(x)=-2sqrt(x)+3 ⇔ y=-2sqrt(x)+3
The obtained equation corresponds with option B.
