6. Graph is increasing over entire domain
If y increases as x increases over the entire domain of the function, it is said to be an increasing function.
Looking at the graphs, we can see that Graphs G and I are increasing.
7. Graph is decreasing over entire domain
If y decreases as x increases over the entire domain of the function, it is said to be a decreasing function.
Looking at the graphs, we can see that Graphs A and F are decreasing.
8. Graph changes from increasing to decreasing atleast one time
From the definition of increasing and decreasing functions above, we will look for atleast one time when a graph is changing slopes, from increasing to decreasing.
Looking at the graphs, we see that Graphs C, K, M, O, P.
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#11 -------------------------------------------------------------------------------
Which of the graphs shown have no roots??
By roots, we mean "solutions". In graphical form, it means the point where it cuts the x-axis.
Let's see which graphs does not cut the x-axis.
Graph H - doesn't go through x axis. So, no root.
Graph P - doesn't go through the x-axis. So, no root.
AnswerGraph H and Graph P#12 -------------------------------------------------------------------------------Which graph has asymptotes?
Asymptotes are lines that a graph never cuts/crosses. They approach asymptotes, but never goes through them.
We will look at the graphs to see which one contains asymptotes.
Graph D - x = π/2, 3π/2 etc. are asymptote lines. So, this graph HAS asymptotes.
Graph H - the x-axis and the y-axis are both asymptotes to this graph. So, this graph HAS asymptotes.
Graph L - the y-axis is an asymptote to the graph.
Graph P - the x-axis is an asymptote. Also, x = π/2, 3π/2 etc. are asymptote lines as well.
AnswerGraph D, Graph H, Graph L, and Graph P