Recognising cubic, reciprocal and exponential graphs

Mathematics · Algebra · ages 15-16

Name ______________________ Date ____________

The reciprocal y = 1/x crosses the x-axis.
Circle one: True False
For y = 1/x, doubling a nonzero input doubles its output.
Circle one: True False
The cubic is an odd shape, so the point (4, 64) on y = x cubed has a partner at:
- (-4, 64)
- (4, -64)
- (-4, -64)
- (-64, -4)
What is 2 to the power of 5?
Answer: ______________
The number of bacteria in a petri dish doubles every hour. Which shape models the bacterial population against time?
- the cubic
- the reciprocal
- the exponential
- a straight line
Calculate the output of y = 3^x at input x = 4.
Answer: ______________
For y = 1/x with a negative input x, which quadrant contains the point?
- The first quadrant
- The third quadrant
- The second quadrant
- The fourth quadrant
What is 2 to the power of -3? Give your answer as a decimal.
Answer: ______________
Translate y = 2^x right by 3. Which equation describes the result?
- y = 2^x + 3
- y = 2^(x-3)
- y = 2^(x+3)
- y = 2^x - 3
Ava says that on y = x cubed, at x = -5, y is 125, because cubing a negative gives a positive. Where is the slip?
- the point should be (5, 125)
- the cubic only takes positive x values
- cubing means squaring twice
- (-5)³ = -125: cubing keeps the sign

Answer key

For grown-ups. Fold this page away before handing over the rest.

False · The curve would cross the x-axis where y = 0, but 1/x never equals 0. It only gets closer and closer.
False · Replacing x with 2x gives 1/(2x), half the original output 1/x.
(-4, -64) · A half turn around the origin flips both coordinates, so (4, 64) pairs with (-4, -64). Indeed (-4) cubed is -64.
32 · 2 to the power 5 is 32, the fifth step of the doubling sequence 1, 2, 4, 8, 16, 32.
the exponential · Each equal time step multiplies the population by the same factor 2. That fixed multiplier gives an exponential model.
81 · Four factors of 3 give 3 times 3 times 3 times 3 = 81.
The third quadrant · A negative input gives a negative reciprocal. Both coordinates are negative, so the point lies in the third quadrant.
0.125 · 2 to the power -3 is 1 over 2 to the power 3, which is 1/8 = 0.125.
y = 2^(x-3) · A right translation replaces the input x with x - 3, giving y = 2^(x - 3).
(-5)³ = -125: cubing keeps the sign · -5 times -5 is 25, and 25 times -5 is -125. Two negatives make a positive, but the third negative brings it back down, so (-5) cubed is -125.