QCE Mathematical Methods Unit 2 Practice questions

Determine the y-intercept of y = 3^x

y-intercept = 1 [This is because x=0, and the index law states that any number to the power of zero equal 1]

Hence or otherwise determine the y - intercept of y = 3^x−3

y-intercept = -2

Determine the horizontal asymptote of y = ​3^x

y = 0 [This is because when x approaches infinity, the value of y approaches 0, indicating the horizontal asymptote.]

Hence or otherwise determine the horizontal asymptote of y = 3^x - 3

y = -3 [3^x = 0 and 0 - 3 = -3]

This is a graph of y = 2^{x ,} How do we shift the graph of y = 2^x to get the graph of y = 2^x− 5?

Move the graph downwards by 5 units

Consider the curve y = 4^x − 5. Determine the y-intercept of the exponential curve.

y-intercept = -4 [4^x = 1. 1 - 5 = -4]

Consider a graph of y = 3^x. How could the graph of y = 3^x+1 be obtained from the graph of y=3^x?

Through a vertical translation