Further Graphs & Tangents Quiz

1. What is the vertical asymptote of $y = \frac{3}{x}$?

• A. $x=0$
• B. $y=0$
• C. $x=3$
• D. $y=3$

2. What is the horizontal asymptote of $y = 4(2)^x - 3$?

• A. $y=4$
• B. $y=2$
• C. $y=-3$
• D. $y=0$

3. Which function type produces a graph with two separate branches that never touch the axes?

• A. Quadratic
• B. Reciprocal
• C. Linear
• D. Cubic

4. What does the gradient of a tangent to a curve at a point represent?

• A. The average rate of change over the whole curve
• B. The instantaneous rate of change at that point
• C. The y-intercept of the curve
• D. The distance from the origin

5. A population model is $P = 200(1.05)^t$. What does the shape of this graph tell you about the population over time?

• A. It decreases and approaches zero
• B. It increases at a constant rate (linear)
• C. It grows, increasingly steeply, with no upper asymptote reached in this model
• D. It oscillates periodically