Question 1: Calculate the value of y when x = 3 for y = 2ˣ.

Answer: 8

Question 2: Plot the graph of y = 3ˣ for x values from -2 to 2.

Answer: Plot points at x = -2, -1, 0, 1, 2 with corresponding y-values 1/9, 1/3, 1, 3, 9.

Question 3: Determine whether the graph y = (1/2)ˣ is increasing or decreasing as x increases.

Answer: Decreasing

Question 4: Find the value of y when x = -1 for y = 4ˣ.

Answer: 0.25

Question 5: Plot the point of y = 5ˣ when x = 0.5 on the graph grid.

Answer: Point at (0.5, approximately 2.24)

Question 6: Compare the growth of y = 2ˣ and y = 3ˣ as x increases. Which grows faster?

Answer: y = 3ˣ grows faster

Question 7: Solve for x: 2ˣ = 16.

Answer: x = 4

Question 8: Construct a graph for y = (1/3)ˣ and label key points.

Answer: Plot points at x = -2, -1, 0, 1, 2 with y-values 3²=9, 3¹=3, 1, 1/3, 1/9.

Question 9: Explain why the graph of y = 2ˣ never touches the x-axis.

Answer: Because y = 2ˣ is always positive for all real x, it never reaches zero or touches the x-axis.

Question 10: Identify the mistake in plotting the exponential y = 5ˣ if a student claims that y = 5ˣ passes through (0,1) and (1,5).

Answer: There is no mistake; y = 5ˣ passes through (0,1) and (1,5).

Question 11: Challenge: Plot y = 2ˣ and y = 0.5ˣ on the same grid for x = -2 to 2. Describe their intersection points if any.

Answer: They intersect at x = 0 where both y = 1.