Compared to the graph of the base function f(x) = √x, the graph of the function g(x) = √x-5 is translated
A. 5 Units Down
B. 5 Units Left
C. 5 Units Right
D. 5 Units Up
√x-5 is translated down 5
√(x-5) is translated right 5
This is math. To get a correct answer, ask the correct question.
Well, since we're dealing with square roots, we can imagine the graph of f(x) = √x as the profile of a happy little hill. Now, let's take a look at g(x) = √x - 5.
To make it clearer, let's focus on the "-5" part. When we subtract 5 from the graph, we're actually moving it down the y-axis. Poof! That happy hill just went downhill. So the correct answer is A. 5 Units Down.
Stay positive, though! Maybe it'll find its smile again!
To determine how the graph of the function g(x) = √x - 5 compares to the graph of the base function f(x) = √x, we need to identify the translation applied to the graph.
Notice that g(x) is obtained from f(x) by subtracting 5 from the output (√x). This translates the graph vertically.
Since we are subtracting 5 from the output, the graph of g(x) will be shifted down by 5 units compared to f(x).
Therefore, the correct answer is:
A. 5 Units Down
To determine the translation of the graph of the function g(x) = √x-5 compared to the graph of the base function f(x) = √x, we need to examine how the function has been modified. In this case, the function g(x) = √x-5 has been horizontally shifted by a value of 5 units to the right.
Explanation:
A function of the form g(x) = f(x-a) represents a horizontal translation of the base function f(x) by a units in the opposite direction. If a is positive, it represents a shift to the right, and if a is negative, it represents a shift to the left.
In the given function g(x) = √x-5, we can identify that the value of a is -5. Since a is negative, it indicates a shift to the left. However, we need to find the absolute value of a, which is |a| = |-5| = 5. Therefore, the graph of g(x) = √x-5 has been translated 5 units to the right from the base function f(x) = √x.
Therefore, the correct answer is C. 5 Units Right.