11.07 Comparing function types
Interactive practice questions
A table of values for the function $P$P and for the function $Q$Q are provided below.
| Function $P$P: | |||||
| $x$x | $-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
| $y$y | $9$9 | $6$6 | $3$3 | $0$0 | $-3$−3 |
| Function $Q$Q: | |||||
| $x$x | $0$0 | $1$1 | $2$2 | $3$3 | $4$4 |
| $y$y | $6$6 | $3$3 | $2$2 | $3$3 | $6$6 |
Which of the following statements are true?
Function $P$P is a line and function $Q$Q is a parabola.
Function $P$P is a parabola and function $Q$Q is a parabola.
Function $P$P is a line and function $Q$Q is a line.
Function $P$P is a parabola and function $Q$Q is a line.
Graph the function $P$P below.
Graph the function $Q$Q below.
Which of the following statements are true?
As $x$x tends to infinity, function $Q$Q is higher than function $P$P.
As $x$x tends to infinity, function $P$P is higher than function $Q$Q.
Which of the following statements is true on the domain $x<2$x<2?
Function $P$P is increasing and function $Q$Q is increasing.
Function $P$P is decreasing and function $Q$Q is increasing.
Function $P$P is decreasing and function $Q$Q is decreasing.
Function $P$P is increasing and function $Q$Q is decreasing.
Consider the line $P$P given by the equation $y=-12+\frac{x}{10}$y=−12+x10, and the table of values for parabola $Q$Q.
The graph of the parabola $P$P is given by $y=-3\left(x-2\right)^2-3$y=−3(x−2)2−3 and the line $Q$Q is given by $y=-6x+12$y=−6x+12.
The line $P$P is given by $y=-4+\frac{4x}{3}$y=−4+4x3 and the parabola $Q$Q is given by $y=-\left(x-1\right)\left(x-4\right)$y=−(x−1)(x−4).