2.05 Comparing functions
Interactive practice questions
Parabola $P$P is given by $y=-\frac{\left(x+2\right)^2}{4}-2$y=−(x+2)24−2 and a table of values for parabola $Q$Q is provided below.
Parabola $Q$Q:
| $x$x | $-1$−1 | $1$1 | $3$3 |
| $y$y | $-2$−2 | $-1$−1 | $-2$−2 |
Graph Parabola $Q$Q below.
Which function has the greatest maximum?
Parabola $P$P
Parabola $Q$Q
Given that we can obtain parabola $Q$Q by translating parabola $P$P to the right by $3$3 places and up by $1$1 place, how many times do the parabolas intersect?
Once
Zero times
Twice
Three times
Which function is decreasing on the domain $-2\le x\le1$−2≤x≤1?
Neither parabola $P$P nor parabola $Q$Q
Parabola $P$P and parabola $Q$Q
Parabola $P$P
Parabola $Q$Q
A table of values for the function $P$P and for the function $Q$Q are provided below.
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.
Consider the functions $f\left(x\right)=2^x$f(x)=2x and $g\left(x\right)=2x^2$g(x)=2x2, for $x\ge0$x≥0.