gaokao 2021 Q12

gaokao · China · national-A-science Function Transformations
12. Let the domain of function $f(x)$ be $\mathbb{R}$. $f(x+1)$ is an odd function, $f(x+2)$ is an even function. When $x \in [1,2]$, $f(x) = ax^2 + b$. If $f(0) + f(3) = 6$, then $f\left(\frac{4}{2}\right) =$
A. $-\frac{9}{4}$
B. $-\frac{3}{2}$
C. $\frac{7}{4}$
D. $\frac{5}{2}$
II. Fill in the Blank Questions (4 questions in total, 5 points each, 20 points total)
12. Let the domain of function $f(x)$ be $\mathbb{R}$. $f(x+1)$ is an odd function, $f(x+2)$ is an even function. When $x \in [1,2]$, $f(x) = ax^2 + b$. If $f(0) + f(3) = 6$, then $f\left(\frac{4}{2}\right) =$\\
A. $-\frac{9}{4}$\\
B. $-\frac{3}{2}$\\
C. $\frac{7}{4}$\\
D. $\frac{5}{2}$

\section*{II. Fill in the Blank Questions (4 questions in total, 5 points each, 20 points total)}