# If 2x 4 20 what does x

### Calculate function values

In a function, each \$\$ x \$\$ value has a \$\$ y \$\$ value.

With the function term you can calculate the \$\$ y \$\$ values. You sit instead of the variable each a number and then calculate the term.

The \$\$ y \$\$ values ​​are also called function values.

Example:
Function: \$\$ f (\$\$\$\$ x \$\$\$\$) = 3 \$\$\$\$ x \$\$ \$\$ - 5 \$\$

You can calculate the function value for \$\$ x = \$\$ \$\$ 5 \$\$ as follows:
\$\$ f (\$\$\$\$ 5 \$\$\$\$) = 3 * \$\$ \$\$ 5 \$\$ \$\$ - 5 = 15 \$\$ \$\$ - 5 = 10 \$\$

You can calculate the function value for \$\$ x = \$\$ \$\$ - 1 \$\$ as follows:
\$\$ f (\$\$\$\$ - 1 \$\$\$\$) = 3 * (\$\$\$\$ - 1 \$\$\$\$) \$\$ \$\$ - 5 = \$\$ \$\$ - 3 \$\$ \$\$ - 5 = \$\$ \$\$ - 8 \$\$

\$\$ x \$\$ - value and \$\$ y \$\$ - value belong together. They form a pair of values ​​or a point.

You write:
The value pairs \$\$ (- 1 | -8) \$\$ and \$\$ (5 | 10) \$\$ belong to the function \$\$ f (x) = 3x-5 \$\$

Doesn't that look like points in the coordinate system? Correct!

This is how it looks in general:

Function equation:
\$\$ y = f (x) = mx + b \$\$ (for each \$\$ x \$\$ value)

Function value for \$\$ x = 2 \$\$:
\$\$ f (2) = m * 2 + b \$\$ (for a certain \$\$ x \$\$ value)

Functional term
┌─┴──┐
\$\$ f (x) = 3x-5 \$\$
└────┬────┘
Function equation

### Value pairs and points

As a graph, linear functions always have a straight line.

You can draw the pair of values ​​\$\$ (x | y) \$\$ as a point in the coordinate system. The value pairs of the function are the points of the straight lines in the coordinate system.

You can draw the straight line with 2 pairs of values ​​or points.

Example:
After \$\$ x \$\$ minutes, the height \$\$ h (x) \$\$ of a candle in cm \$\$ h (x) = \$\$ \$\$ - 2/3 x + 20 \$\$.

To draw the straight line, calculate 2 points that are not too close together.

You reckon:
\$\$ h (0) = - 2/3 * 0 + 20 = 20 \$\$ \$\$ rarr \$\$ point \$\$ (0 | 20) \$\$
\$\$ h (30) = - 2/3 * 30 + 20 = –20 + 20 = 0 \$\$ \$\$ rarr \$\$ point \$\$ (30 | 0) \$\$

\$\$ x \$\$ - coordinate
\$\$ darr \$\$
Dot \$\$ (\$\$\$\$ 2 \$\$\$\$ | \$\$\$\$ 3 \$\$\$\$) \$\$
\$\$ uarr \$\$
\$\$ y \$\$ - coordinate

Here the function is not called \$\$ f \$\$, but \$\$ h \$\$. Instead of \$\$ f \$\$ for any function, one chooses \$\$ h \$\$ for the function equation of the height.

### The other way around: Calculate \$\$ x \$\$ values

It is a bit more difficult when the \$\$ y \$\$ is given and you have to calculate the corresponding \$\$ x \$\$.

Incidentally, the \$\$ x \$\$ values ​​are called arguments.

Example:

Function: \$\$ f (x) = 3x \$\$ \$\$ - 5 \$\$

What is the name of the \$\$ x \$\$ value for the function value \$\$ 4 \$\$?

Mathematically: For which \$\$ x \$\$ is \$\$ f (x) = 4 \$\$?

\$\$ 3x-5 = 4 \$\$ \$\$ | \$\$ \$\$ + 5 \$\$

\$\$ 3x = 9 \$\$ \$\$ | \$\$ \$\$: 3 \$\$

\$\$ x = 3 \$\$

The function value \$\$ y = 4 \$\$ includes \$\$ x = 3 \$\$.

A \$\$ x \$\$ value is also called argument or abscissa (from lat. linea abscissa "Cut line")

A \$\$ y \$\$ value is also called ordinate (from lat. linea ordinata "Orderly line")

\$\$ y \$\$ is dependent on \$\$ x \$\$ - as a donkey bridge for the names you can stick to the order in the alphabet:
A before O as well as \$\$ x \$\$ before \$\$ y \$\$.

kapiert.decan do more:

• interactive exercises
and tests
• individual classwork trainer
• Learning manager

Anna helps out on the strawberry field during the holidays. She collects the prices for self-picked strawberries.

• \$\$ 1 \$\$ kg strawberries costs \$\$ 2.50 \$\$ \$\$ € \$\$.
• Each customer pays an additional \$\$ 0.50 \$\$ \$\$ € \$\$ to allow them to nibble a little while picking.

Anna writes down the functional equation \$\$ y = f (x) = 2.5 * x + 0.5 \$\$ and calculates different pairs of values.

Example 1:
How much do \$\$ 2 \$\$ kg of picked strawberries cost?
\$\$ y = f (2) = 2.5 * 2 + 0.5 = 5.5 \$\$

\$\$ 2 \$\$ kg of picked strawberries cost \$\$ 5.50 \$\$ \$\$ € \$\$.

Example 2:
Mr. Lu pays \$\$ 13.00 \$\$ \$\$ £ \$\$. How many kg of strawberries did he pick?

\$\$ y = f (x) = 13.00 \$\$

\$\$ 2.5 * x + 0.5 = 13.00 \$\$ \$\$ | \$\$ \$\$ - 0.5 \$\$

\$\$ 2.5 * x = 12.50 \$\$ \$\$ | \$\$ \$\$: 2.5 \$\$

\$\$ x = 5 \$\$

Mr. Lu picked \$\$ 5 \$\$ kg of strawberries.

### Table of values

So that Anna doesn't have to calculate every time, she has created a table of values:

\$\$ y = f (x) = 2.5 * x + 0.5 \$\$

Weight in kg (\$\$ x \$\$)Price in euros (\$\$ y \$\$)
\$\$1,0\$\$
\$\$3,00\$\$
\$\$1,5\$\$
\$\$4,25\$\$
\$\$2,0\$\$
\$\$5,50\$\$
\$\$2,5\$\$
\$\$6,75\$\$
\$\$3,0\$\$
\$\$8,00\$\$
\$\$3,5\$\$
\$\$9,25\$\$
\$\$4,0\$\$
\$\$10,50\$\$
\$\$4,5\$\$
\$\$11,75\$\$
\$\$5,0\$\$
\$\$13,00\$\$

The graph for this:

A Table of values is clear if you more than 2 Calculate points of the graph.

##### Tip calculator:

Some pocket calculators do the arithmetic for a table of values ​​for you - take a look at the instructions for use!

### A bit of theory at the end

#### Domain of definition

The domain of definition are all numbers that you can insert into a function, i.e. all \$\$ x \$\$ values.

For linear functions: \$\$ D = QQ \$\$

#### Range of values

The domain of definition are function values ​​(\$\$ y \$\$ values) that can come out when calculating the function term.

For linear but not constant functions: \$\$ W = QQ \$\$

\$\$ QQ \$\$ are the rational numbers: all positive and negative fractions.

kapiert.decan do more:

• interactive exercises
and tests
• individual classwork trainer
• Learning manager