Functions and Graphs 2

Question 1

What is ALWAYS used to write where a graph is increasing, decreasing, or remains constant.

Answer 1

Open intervals on the x-axis (because behavior at endpoints is excluded).

Question 2

From what to what direction should evaluation of a graph happen when determining the increasing, decreasing, or constant states of a graph?

Answer 2

From left to right.

Question 3

What’s a relative maximum in a graph?

Answer 3

A relative maximum is the greatest y value in a local(small) area of a graph. It is called relative, or local, because it doesn’t relate to the whole graph but for a small portion of it instead.

Question 4

What is reffered to as a relative “peak” in graphs?

Answer 4

The relative maximum of that specific area.

Question 5

What’s a relative minimum?

Answer 5

A point on a graph where the graph goes from decreasing to increasing. Aka the lowest point.

Question 6

What’s used as an answer when asked for the location of a relative maximum/minimum?

Answer 6

The x value of that specific point.

Question 7

What’s used as an answer when asked for the relative maximum of a specific point?

Answer 7

The y value of that point.

Question 8

What does the word “symmetria” mean?

Answer 8

The same measure.

Question 9

Find the relative maximum and its location for the function f(x) = x^3-3x.

Answer 9

Relative maximum location -1, the value of the relative maximum = 2.

Question 10

What’s the definition for a symmetric graph with respect to the y-axis?

Answer 10

A graph is symmetric with respect to the y-axis if for every (x,y) point on the graph, the point (-x,y) is also on the graph.

Question 11

What’s the definition for a symmetric graph with respect to the x-axis?

Answer 11

A graph is symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x,-y) is also on the graph.

Question 12

What’s the definition for a symmetric graph with respect to the origin?

Answer 12

A graph is symmetric with respect to the origin if for every (x,y) point, the point (-x,-y) is also on the graph.

Question 13

With respect to what is the graph of the function f(x) symmetric if f(-x) = f(x)?

Answer 13

To the y-axis.

Question 14

Using the equation of a function, how do we test if a function is symmetric with respect to the y-axis? Use f(x) = x^2 for your explanation.

Answer 14

Replace x with -x in the equation, if the new equation is equivalent, then the function’s graph is symmetrical in respect to the y-axis.

y = x^2,
y = (-x)^2 = x^2,
(y=x^2) = (y=(-x^2)), the function’s graph is symmetrical to the y-axis.

Question 15

What type of symmetric graph is not a function?

Answer 15

Graph symmetric with respect to the x-axis.

Question 16

Using the equation of a graph, how do we test if it is symmetric with respect to the origin?
Use this equation for your example: y^2 = x^2 + 2

Answer 16

We substitute x with -x and y with -y, if we get an equivalent equation, then the graph is symmetric with respect to the origin.

Question 17

How is a function called if its graph is symmetric with respect to the y-axis?

Answer 17

An even function.

Question 18

How is an even function defined? Give an example with a function that satisfies the definition.

Answer 18

The function f is an even function if f(-x) = f(x).
Example: f(x) = x^2, f(-x) = (-x)^2 = x^2, f(x) = f(-x).

Question 19

How is a function called if its graph is symmetric with respect to the origin.

Answer 19

An odd function.

Question 20

What’s the definition for an odd function? Give an example with a function that satisfies the definition.

Answer 20

The function f is odd if f(-x) = -f(x).
Example: f(x) = x^3 + x,
f(-x) = -x^3 - x,
-f(x) = -(x^3 + x), f(x) = -x^3 - x,
-f(x) = f(-x).

Question 21

Instead of using the definition for an odd function, what’s a quicker way to determine if a function is odd?

Answer 21

By looking at the function’s equation’s terms. If each term’s exponent is an odd number, then this function is odd.

Question 22

Instead of using the definition for an even function, what’s a swifter way to determine if a function is even?

Answer 22

By looking at the function’s equation’s terms. If each term’s exponent is an even number, then this function is even.

Question 23

What’s a piecewise function?

Answer 23

A function that is defined by two or more equations over a specified domain.

Question 24

What’s a “greatest integer function”?

Answer 24

A function that gives the greatest integer which is less than or equal to x.