Use the graph of the parent function, f left-parenthesis x right-parenthesis equals Start Root x End Root, to describe the transformation for the graph of g left-parenthesis x right-parenthesis equals Start Root x minus 5 End Root.

Answer 1

The graph of the parent function f(x) = √x is a simple square root function. The graph starts at the point (0, 0) and has a horizontal asymptote at y = 0. As x increases, y also increases but at a decreasing rate.

The transformation g(x) = √(x - 5) shifts the graph of the parent function 5 units to the right. This means the graph will now start at the point (5, 0) instead of (0, 0). The horizontal asymptote remains at y = 0, and as x increases, y also increases but at a slower rate compared to the graph of f(x).

In summary, the graph of g(x) = √(x - 5) is a shifted and slightly compressed version of the graph of f(x) = √x.

Answer 2

Which function transforms the graph of f left-parenthesis x right-parenthesis equals x superscript 5 baseline by shifting it up 6 units?
options

a) g left-parenthesis x right-parenthesis equals x superscript 5 baseline plus 6Image with alt text: g left-parenthesis x right-parenthesis equals x superscript 5 baseline plus 6

b) g left-parenthesis x right-parenthesis equals x superscript 5 baseline minus 6
Image with alt text: g left-parenthesis x right-parenthesis equals x superscript 5 baseline minus 6

c) g left-parenthesis x right-parenthesis equals left-parenthesis x plus 6 right-parenthesis superscript 5 baseline
Image with alt text: g left-parenthesis x right-parenthesis equals left-parenthesis x plus 6 right-parenthesis superscript 5 baseline

d) g left-parenthesis x right-parenthesis equals left-parenthesis x minus 6 right-parenthesis superscript 5 baseline

Answer 3

The correct option is:

c) g(x) = (x + 6)^5