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Review Chapter 4 Sections 1-6

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The Coordinate Plane 4-1

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**Vocabulary Axes Origin Coordinate plane Y-axis X-axes X-coordinate**

Y-coordinate Quadrant Graph

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**The Coordinate Plane Axes – two perpendicular number lines.**

Origin – where the axes intersect at their zero points. X-axes – The horizontal number line. Y-axis – The vertical number line. Coordinate plane – the plane containing the x and y axes. 1 2 3 4 5 -1 -2 -3 -4 -5 y x 1 2 3 4 5 -1 -2 -3 -4 -5 Origin (0,0)

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Quadrants 1 2 3 4 5 -1 -2 -3 -4 -5 y Quadrants – the x-axis and y-axis separate the coordinate plane into four regions. Notice which quadrants contain positive and negative x and y coordinates. II I (–,+) (+,+) x 1 2 3 4 5 -1 -2 -3 -4 -5 III IV (–, –) (+, –)

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**Coordinates (2, 3) (2, 3) (0, 0) origin move right 2 units**

1 2 3 4 5 -1 -2 -3 -4 -5 y To plot an ordered pair, begin at the origin, the point (0, 0), which is the intersection of the x-axis and the y-axis. (2, 3) (0, 0) x The first coordinate tells how many units to move left or right; the second coordinate tells how many units to move up or down. 1 2 3 4 5 -1 -2 -3 -4 -5 origin move right 2 units (2, 3) move up 3 units x-coordinate move right or left y-coordinate move up or down To graph an ordered pair means to draw a dot at the point on the coordinate plane that corresponds to the ordered pair.

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**Transformations on the Coordinate Plane**

4-2

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**Vocabulary Transformation – movements of geometric figures**

Preimage – the position of the figure before the transformation Image – the position of the figure after the transformation. Reflection – a figure is flipped over a line (like holding a mirror on it’s edge against something) Translation – a figure is slid in any direction (like moving a checker on a checkerboard) Dilation – a figure is enlarged or reduced. Rotation – a figure is turned about a point.

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**Types of Transformations**

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**Reflection and Translation**

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Dilation and Rotation

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Relations 4-3

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**Vocabulary Mapping – a relation represented by a set of ordered pairs.**

Inverse – obtained by switching the coordinates in each ordered pair. (a,b) becomes (b,a) Relation – a set of ordered pairs

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**Mapping, Graphing, and Tables**

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Mapping the Inverse

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**Equations as Relations**

4.4

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Vocabulary Equation in two variables – an equation that has two variables Solution – in the context of an equation with two variables, an ordered pair that results in a true statement when substituted into the equation.

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**Different Ways to Solve**

Solving using a replacement set – a variation of guess and check. You start with an equation and several ordered pairs. You plug each ordered pair into the equation to determine which ones are solutions. Solving Using a Given Domain – Start with an equation and a set of numbers for one variable only. You then substitute each number in for the variable it replaces, and solve for the unknown variable. This gives you a set of ordered pairs that are solutions.

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Dependent Variables When you solve an equation for one variable, the variable you solve for becomes a “Dependent Variable”. It depends on the values of the other variable. Dependent Variable Independent Variable The values of “y” depend on what the value of “x” is.

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**Graphing Linear Equations**

4.5

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**Vocabulary Linear equation – the equation of a line**

Standard form – Ax + By = C where A, B, and C are integers whose greatest common factor is 1, A is greater than or equal to 0, and A and B are both not zero. X-intercept – The X coordinate of the point at which the line crosses the x-axis (Y is equal to 0) Y-intercept – the Y coordinate of the point at which the line crosses the y-axis (X is equal to 0)

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**Methods of Graphing Make a table – Use the Intercepts –**

Solve the equation for y. Pick at least 3 values for x and solve the equation for the 3 values of y that make the equation true. Graph the resulting x and y (ordered pair) on a coordinate plane. Draw a line that includes all points. Use the Intercepts – Make X equal to zero. Solve for Y. Make Y equal to zero. Solve for X. Graph the two coordinate pairs: (0,Y) and (X,0) Draw a line that includes both points.

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Functions 4.6

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Vocabulary Function – a relation in which each element of the domain is paired with exactly one element of the range (for each value of x there is a value for y, but each value of y cannot have more than one value of x) Vertical line test – if no vertical line can be drawn so that it intersects the graph in more than one place, the graph is a function Function notation – f(x) replaces y in the equation.

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Vertical Line Test

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Function Notation f(5) =3(5)-8 =15-8 =7

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**Other Functions and Notations**

Non-Linear Functions – Functions that do not result in a line when plotted. Alternative Function Notation – another way of stating f(x) is <<x>>.

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