149k views
2 votes
How does the graph of g(x) = 25 - x relate to the graph of the parent function, f(x) = √x?

a) The graph of g(x) is shrunk vertically by a factor of 25
b) The graph of g(x) is stretched vertically by a factor of 25
c) The graph of g(x) is shrunk vertically by a factor of √25
d) The graph of g(x) is stretched vertically by a factor of √25

1 Answer

3 votes

Final answer:

The graph of g(x) = 25 - x is a linear function and is not a transformation of the parent function f(x) = √x; it is a downward sloping line, while f(x) is an increasing curve.

Step-by-step explanation:

The function g(x) = 25 - x is not a transformation of the parent function f(x) = √x. Instead, g(x) is a linear function, whereas f(x) is a radical function. The two functions have different shapes and characteristics. The parent function f(x) = √x is the graph of a square root, which results in a curve that starts at the origin (0,0) and increases to the right. The graph of a square root function is always increasing, slowly at first and then more rapidly as x increases.

On the other hand, g(x) = 25 - x is a linear function with a y-intercept of 25 and a slope of -1. It is a straight line that starts at (0, 25) and decreases as x increases, sloping downwards to the right. This graph has no stretching or shrinking in relation to f(x) = √x because the two functions are fundamentally different in form and do not share a direct algebraic transformation. Answer choices a, b, c, and d are not applicable because they describe transformations of the √x function, which is not the case for g(x).

User ZigZagZebra
by
8.2k points