I can help — do you want (A) a practice quiz with answers, (B) step-by-step solutions to specific problems, or (C) a focused explanation of graphing transformations? If you pick one, I’ll tailor the help.
Below is a short practice quiz (5 questions) plus answers and brief explanations so you can check which option you want next.
Mini Quiz — Graphing Functions
Q1. Describe the graph of $y=(x-2)^2+3$. Give the vertex and the transformation from $y=x^2$.
Q2. Describe the graph of $y=-2|x+1|+4$. Give the vertex and transformations from $y=|x|$.
Q3. Describe one period and key shifts for $y=\sin\big(x-\tfrac{\pi}{2}\big)$ compared to $y=\sin x$.
Q4. Sketch (describe) the line $y=\tfrac{1}{2}x-1$. Give slope and $y$-intercept.
Q5. If $y=f(x)$ is given, how does the graph of $y=f(-x)+2$ relate to $y=f(x)$?
Answers and Brief Explanations
A1. The vertex is $(2,3)$. Transformation: translate $y=x^2$ right 2 units and up 3 units. (No reflection or stretch.)
A2. Vertex is $(-1,4)$. Transformations from $y=|x|$: reflect across the $x$-axis (the negative sign), vertical stretch by factor 2, translate left 1, translate up 4. So it is a V-shape opening downward, steeper than $y=|x|$.
A3. $y=\sin\big(x-\tfrac{\pi}{2}\big)$ is $\sin x$ shifted right by $\tfrac{\pi}{2}$. One period is $2\pi$; for example the interval $[\tfrac{\pi}{2},\tfrac{5\pi}{2}]$ is one period with the same shape as $[0,2\pi]$ of $\sin x$.
A4. Slope is $\tfrac{1}{2}$, $y$-intercept is $-1$. So it rises one unit for every two units right; points: $(0,-1)$, $(2,0)$, $(-2,-2)$.
A5. $y=f(-x)+2$ is the graph of $f$ reflected across the $y$-axis (replace $x$ with $-x$), then translated up 2 units.
If you want, I can:
- Provide full sketches (images) or step-by-step graphing instructions for each question.
- Make a longer quiz with answers and detailed solutions.
- Work through a specific problem you’re stuck on — paste it here. Which would you like?