Linear functions/translation of graphs

In summary, a linear function is a mathematical function represented by a straight line on a graph, following the form y = mx + b. To graph a linear function, points can be plotted and connected or the slope and y-intercept can be used to draw the line. Translation of a graph involves moving it to a different location using horizontal or vertical shifts or reflections. Linear functions and translations are related as they both involve manipulating the position of a graph on a coordinate plane. This understanding is important in analyzing and interpreting graphs in mathematics and other fields of science.
  • #1
TMNT
25
0
The question is

Graph f(x)=X^3-3x. Does it have any high or low points? What about symmetry?

Okay the problem I'm having is what formula to use with a ^3 on the X, my previous 2 problems I did by using the quad formula, those questions were f(x)= 2x^4+4x^2-1, and f(x)= 16x^2+4x-3 respectively.
 
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  • #2
f(x)= x^3- 3x= x(x^2- 3). What values of x makes f(x)= 0? What happens between those values of x?
 
  • #3
What about symmetry?

f(x) = f(-x)?

f(-x) = -f(x)?
 

Related to Linear functions/translation of graphs

1. What is a linear function?

A linear function is a type of mathematical function that can be represented by a straight line on a graph. It follows the general form of y = mx + b, where m is the slope of the line and b is the y-intercept. Linear functions are often used to model real-world relationships between two variables.

2. How do you graph a linear function?

To graph a linear function, you can plot points on a coordinate plane and then connect them with a straight line. Alternatively, you can use the slope and y-intercept to find two points on the line and then draw the line through them. Another method is to use the x and y intercepts to plot two points and then connect them with a line.

3. What is translation of a graph?

Translation of a graph refers to the process of moving a graph to a different location on a coordinate plane. This can be done by shifting the graph horizontally or vertically, or by reflecting it across an axis. Translation does not change the shape of the graph, but it changes its position.

4. How do you translate a graph?

To translate a graph, you can use the translation rules for horizontal and vertical shifts. A horizontal shift is represented by adding or subtracting a value from the x-coordinate of each point on the graph. A vertical shift is represented by adding or subtracting a value from the y-coordinate. Reflections can be done by multiplying the x or y-coordinate by -1.

5. How are linear functions and translations related?

Linear functions and translations are related because they both involve manipulating the position of a graph on a coordinate plane. Linear functions can be translated by changing the slope or y-intercept, while translation involves shifting the entire graph. Understanding the relationship between linear functions and translations is important in analyzing and interpreting graphs in mathematics and other fields of science.

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