Given the graph of f(x)=x2, which of the following expressions is the graph g(x) in terms of f(x)?
Two functions are graphed on a four quadrant coordinate plane. The horizontal x-axis and the vertical y-axis go from negative 5.5 to 5.5 in increments of 1. A U-shaped graph labeled f left parenthesis x right parenthesis that opens upward has a vertex at left parenthesis 0 comma 0 right parenthesis and passes through left parenthesis negative 1 comma 1 right parenthesis and left parenthesis 1 comma 1 right parenthesis. A second U-shaped graph labeled g left parenthesis x right parenthesis that opens downward has a vertex at left parenthesis 0 comma 1 right parenthesis and passes through left parenthesis negative 1 comma 0 right parenthesis and left parenthesis 1 comma 0 right parenthesis.
(1 point)
Responses
g(x)=f(−x)−1
g left parenthesis x right parenthesis equals f left parenthesis minus x right parenthesis minus 1
g(x)=1−f(x)
g left parenthesis x right parenthesis equals 1 minus f left parenthesis x right parenthesis
g(x)=f(x)−1
g left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus 1
g(x)=−f(x)−1
g(x)=f(x)-1
To determine the expression for the graph g(x) in terms of f(x), we need to understand the relationship between the two graphs.
From the given information, we can see that the graph of f(x)=x^2 is a U-shaped graph that opens upward and has a vertex at (0, 0), passing through (-1, 1) and (1, 1). This means that the y-values of f(x) are always positive or zero.
On the other hand, the graph of g(x) is also a U-shaped graph but opens downward. It has a vertex at (0, 1) and passes through (-1, 0) and (1, 0). This means that the y-values of g(x) are always negative or zero.
From this comparison, we can conclude that the graph of g(x) is obtained by reflecting the graph of f(x) vertically and then shifting it downward by 1 unit, since the y-values of f(x) are positive and the y-values of g(x) are negative. Therefore, the correct expression for g(x) in terms of f(x) is:
g(x) = -f(x) - 1
The correct expression for g(x) in terms of f(x) is:
g(x) = 1 - f(x)