Fill in the blank(s) to correctly complete each sentence.

Question

The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.

Accepted Answer

Welcome back, everyone. If the function H of X is equal to -2 x 2 is graphed, how does it graph compared to the graph of Y equals 2 X2? We're given four answer choices A says reflected across the y axis, B stretched vertically by a factor of 2, C reflected across the x axis, and D translated by 2 units downward. So we're given H of X. Which is equal to -2 x 2. And we're also given a y. Let's label it as G of X, another function, which is 2 x squared. Let's notice that they only differ by the negative sign in front of the function. So H of X is simply negative G of X. Now, by definition, whenever we have two functions such as F of X, is equal to negative G of X. They correspond to a reflection across the x axis. By adding a negative sign in front of a function, we are simply reflecting the original function relative to the x axis. So essentially this relationship tells us that j of X. I F of X. Reflected Across The x-axis. And this is exactly what we have. So the given function H of X. Is reflected. Or basically is G of X. Reflected across the x axis. And we can easily check that, right? If the original function is 2 X2, and the new function is -2 X2, for every X that we choose, the Y values are going to be opposite, right, because they're saying negative sign. So the correct answer to this problem corresponds to the answer choice C reflected across the x axis. Thank you for watching.

Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.

Key Concepts

Reflection in Geometry

Square Root Function

Transformations of Functions

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