1.3 Properties of Functions and Graphs

Question 1

line symmetry

Answer 1

a line that divides the graph into two parts such that each part is a reflection of the other

Question 2

point symmetry

Answer 2

a graph is symmetrical about a point if each part of the graph on one side can be rotated 180 degrees to concise with the point on the other side

Question 3

end behaviour

Answer 3

what is happening to the graph as x approaches positive infinity and negative infinity

Question 4

intervals of increase

Answer 4

the intervals within a function’s domain where the y values get larger moving from left to right

Question 5

intervals of decrease

Answer 5

intervals within a function’s domain where the y values get smaller moving from left to right

if the parabola hits the y axis starting from the bottom to top the interval of decrease will be (-infinity, 0)

Question 6

odd function

Answer 6

a function is odd when f(−x)=−f(x) when every term in the function changes sign

if one term changes sign and the rest do not, the function is not odd

Question 7

even function

Answer 7

if you substitute negative x for -x and the new function look like the old function

f(x)=f(-x)

Question 8

when is a function neither odd nor even

Answer 8

when you plug in f(-x) and do not get -f(x) or f(x)

Question 9

even graph

Answer 9

if there’s symmetry about the y axis

Question 10

asymptote

Answer 10

imaginary lines in a graph that can never be touched as a variable (line) approaches infinity

asymptotes are used for rational functions