Graphs of Functions Quiz

1. What shape is the graph of a quadratic function?

• A. A straight line
• B. A parabola
• C. A hyperbola
• D. An S-shaped curve

2. For the graph $y = k^x$ with $k > 0$, which point does the curve always pass through?

• A. $(1, 0)$
• B. $(0, 0)$
• C. $(0, 1)$
• D. $(k, 1)$

3. What are the asymptotes of the reciprocal graph $y = \dfrac{k}{x}$?

• A. $y=x$ and $y=-x$
• B. $x=0$ and $y=0$
• C. $x=1$ and $y=1$
• D. There are no asymptotes

4. By completing the square, what is the turning point of $y = x^2 - 4x + 7$?

• A. $(2, 3)$
• B. $(-2, 3)$
• C. $(4, 7)$
• D. $(2, 7)$

5. A cubic graph $y = ax^3+bx^2+cx+d$ with $a>0$ has turning points at $x=-1$ and $x=3$. Which statement must be true?

• A. The graph has exactly one $x$-axis crossing
• B. The graph has a local maximum at $x=-1$ and a local minimum at $x=3$
• C. The graph has a local minimum at $x=-1$ and a local maximum at $x=3$
• D. The graph is monotonic between $x=-1$ and $x=3$