Question

Match the graphs to the correct function.
$f\left(x\right)=\cos x,g\left(x\right)=f(-x),h\left(x\right)=-f\left(x\right),$
$u\left(x\right)=-g\left(x\right)+3,v\left(x\right)=3h(x+5)$

• A. $u\left(x\right)=-g\left(x\right)+3$
• B. $v\left(x\right)=3h\left(x\right)+5$
• C. $h\left(x\right)=-f\left(x\right)$

Answer 1

The graph of $f\left(x\right)=\cos x$
The graph of $g\left(x\right)=f(-x)$ is the graph of $f\left(x\right)$ flipped over the y-axis,
We observe that $g\left(x\right)=f\left(x\right)$
The graph of $h\left(x\right)=-f\left(x\right)$ is the graph of $f\left(x\right)$ flipped over the x-axis,
Graph of $u\left(x\right)$ is the graph of $-g\left(x\right)+3$ which is the same as graph of $-f\left(x\right)+3$ which is further same as the graph of $h\left(x\right)+3$. So we shift $h\left(x\right)$ upwards by $3$ units
Graph of $v\left(x\right)$ is the graph of $h\left(x\right)$ stretched along the y-axis by $3$ units and shifted upwards by $5$ units