Exponentials

Question 0

e^(lnx) = x

Answer 0

ln[e(^x)] = x

Question 1

y=e(^x)

Answer 1

x = lnx

Question 2

In the graph y = e(^x), what would transforming to y = e(^2x) do?

Answer 2

The curve curves upwards more, steeper

Question 3

In the graph y = e(^x), what would transforming to y = e(^-x) do?

Answer 3

Reflect the graph in the y axis, curve would go backwards:
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\______ instead of _____/

Question 4

In the graph y = e(^x), what would transforming to y = 10e(^x) do?

Answer 4

The graph would cross the y axis at (0,10) rather than (0,1). Steeper.

Question 5

In the graph y = e(^x), what would transforming to y = 3 + 4e(^1/2x) do?

Answer 5

Times y value by 4 so it crosses the y axis at (0,4). Move all values up by 3 so that the y value is (0,7) and the curve tends towards the line x=3 instead of x=0. Draw the curve a lot less steeply as the power is 1/2: half as steep.

Question 6

How would you draw the graph of y=lnx?

Answer 6

Reflect the graph of y=e(^x) in the line y=x.
Passes through the point (1,0) on x axis rather than crossing y axis.
Tends towards y=0 as opposed to x=0.
Domain is all positive numbers ( y > 0), range is all real numbers.

Question 7

What is lnx?

Answer 7

The inverse to e(^x), like how 4 and -4 are opposites

Question 8

What is the range and the domain of the graph y = e(^x) ?

Answer 8

Domain is all real numbers

Range is f(x) > 0