Determine the domain and the range of the function.
-$$f ( x ) = - x ^ { 2 } + 2 x$$
A) domain: $\{ x \mid x \leq 1 \}$
range: $\{ y \mid y \leq 1 \}$

B) domain: all real numbers
range: $\{ y \mid y \leq 1 \}$

C) domain: $\{ x \mid x \leq - 1 \}$
range: $\{ y \mid y \leq 1 \}$

D) domain: all real numbers
range: $\{ y \mid y \leq - 1 \}$

Question

Determine the domain and the range of the function.
-$$f ( x ) = - x ^ { 2 } + 2 x$$
A) domain: $\{ x \mid x \leq 1 \}$
 range: $\{ y \mid y \leq 1 \}$

B) domain: all real numbers 
range: $\{ y \mid y \leq 1 \}$

C) domain: $\{ x \mid x \leq - 1 \}$
 range: $\{ y \mid y \leq 1 \}$

D) domain: all real numbers 
range: $\{ y \mid y \leq - 1 \}$

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers because there are no restrictions on the values of $x$. The vertex form of the given function is $f(x) = -(x-1)^2 + 1$, indicating the vertex is at $(1, 1)$ and the parabola opens downwards. Thus, the maximum value of $y$ is 1, leading to the range $\{ y \mid y \leq 1 \}$.

Determine the Domain and the Range of the Function f(x)=−x2+2xf ( x ) = - x ^ { 2 } + 2 xf(x)=−x2+2x

Determine the Domain and the Range of the Function $f ( x ) = - x ^ { 2 } + 2 x$