Question

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=√(-x+1)

Accepted Answer

Start by graphing the parent function $$ f(x) = \sqrt{x} . $$This is the basic square root function, which starts at the origin (0, 0) and increases gradually as x increases. The domain of this function is $$ x \geq 0 $$, and the range is $$ y \geq 0 . $$Next, analyze the given function $$ h(x) = \sqrt{-x + 1} . $$Rewrite it as $$ h(x) = \sqrt{-(x - 1)}  to $$make the transformation clearer. This shows that the function involves a horizontal shift and a reflection. The term $$ -(x - 1) $$ indicates two transformations: (1) a horizontal reflection across the y-axis due to the negative sign in front of $$ x $$, and (2) a horizontal shift to the right by 1 unit because of $$ x - 1 . $$Apply these transformations to the graph of $$ f(x) = \sqrt{x} $$: (1) Reflect the graph of $$ \sqrt{x} $$ across the y-axis, and (2) shift the resulting graph 1 unit to the right. This gives the graph of $$ h(x) = \sqrt{-(x - 1)} . $$Finally, determine the domain and range of $$ h(x) . $$The domain is restricted by the square root: $$ -(x - 1) \geq 0 $$, which simplifies to $$ x \leq 1 . $$The range remains $$ y \geq 0 $$, as square root values are always non-negative.

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=√(-x+1)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Square Root Function

Graph Transformations

Function Composition