Parametric graphs and the exponential function
Answers are for parents and teachers.
1
Eliminate t from x = 2t − 1, y = t + 5 and find the relation between x and y.
2y = x + 11
2
What curve is x = 3 + 2 cos t, y = −1 + 2 sin t? State its centre and radius.
A circle (x − 3)² + (y + 1)² = 4: centre (3, −1), radius 2.
3
Which is larger: (2/3)^(1/2) or (2/3)^(1/3)?
(2/3)^(1/3)
4
Compute 9^(3/2).
27
5
Is y = 2 − (1/2)ˣ increasing or decreasing? Explain.
Increasing: (1/2)ˣ is decreasing and subtracting it reverses the inequality: x₁ < x₂ gives (1/2)^x₁ > (1/2)^x₂, so 2 − (1/2)^x₁ < 2 − (1/2)^x₂.