Algebra 1 Math Quiz #1 on topics 4.1-4.4

Not a Function

"curved" lines and vertical lines. Functions CANT have repeated X's.

ordered pair

(x,y) coordinate points

How to graph a function

1) sub in the X's. You use the x's given by the domain to sub the Xs with. 2) solve for y. 3) Graph(if needed).

How many quadrants are there?

4 quadrants

Unit Rate

A rate with a denominator of 1. Overall, its the Quantity/1.

Rate of change

Compares a change in one quantity to a change in another quantity. Has two forms, graphically and algebraically.

How to solve a linear function

Determine if the x and y chart have a constant rate of change. Look at #'s and mark the change for x and y. Afterword, pair the change in x and the change in y. If a section(s) equal the same result it IS a linear function. It's not a function even if there's one different result, it IS NOT a constant rate of change.

How to graph an equation

First, create your own x-values to sub in because the domain is normally not given for equations. You must pick 3 x values, no less than that. Always pick X, never Y! You need to have an x value that's negative, positive, or zero. Second, you solve like an equation and record your points using an x and y T-chart. Third, Graph if needed.

How to graph a linear function.

First, you sub in the x's with the domain. The domain would be written differently, EX: domain x is greater than or equal to 0. Afterward, you choose the x value that fits with what the domain is asking you to do. Second, solve for y, just like an equation would ask you to do. Finally, graph if needed.

X-coordinate

Found on X-axis, which is the horizontal line on the graph. is always written first.

y-coordinate

Found on Y-axis, which is the vertical line on the graph. Is Always written second.

x-intercept

Graph intersects the x-axis, making Y ALWAYS equal zero!

y-intercept

Graph intersects the y-axis, making X ALWAYS equal zero!

Negative slope

Known as a DECREASING function. The line falls from left to right. Imagine the line going downhill like a roller coaster.

positive slope

Known as an INCREASING function. the slope of a line going up to the right. Imagine the line going up like an ascending roller coaster.

How to find the intercepts for Y (on a graph)

Label your work as "Y-unit:" For the Y UNIT, sub in zero for x and solve for y. solve like a normal equation. Then write your final answer as a point. EX: (0,-16).

distance-time functions

May be linear, non-linear, increasing, decreasing, or constant depending on the type of movement. To describe a 'distance-time function,' tell 1) where the object starts, (2) what direction it moves, 3) how fast it moves and 4) whether it is speeding up, slowing down or moving at a steady rate(or being still). Our INDEPENDENT variable is X which equals time. Our DEPENDENT variable is Y which equals distance.

How to find the intercepts for X(on a graph)

Organize work by choosing which unit to solve for first by labeling your work "X-unit:" For the X UNIT, sub in zero for y and solve for x. Solve like a normal equation. Write the final answer as a point. EX: (4,0).

Rate of Change Graphically

Ryse/Run. (Ryse over Run).

What does an Undefined/Zero slope problem look like?

The equation would like like this x = a number. EX: x = -2. You Don't need to write a t-chart for undefined graphs, you just plot the point! You plot -2 which would be (-2,0) on the graph and create a vertical line. SAME w/ Zero-Slopes! their problems would look like y=#. You plot (0,#) on the graph and then draw a horizontal line.

How to know if a line is Steep or Not

The number itself determines steepness. EX: A: m=-3 or B: m=1/2. A is steeper because the number, 3, is greater than 1/2. Positive/negative symbol DO NOT determine steepness! +/- determine the direction of the line. An undefined Line is the steepest line you can get.

Slope

The ration of the vertical change(the ryse) to the horizontal change (the run) between any two points on a straight line, represented by m. (or linear functions have a constant rate of change). Slope = Y/X = change in y over change in x.

motion graph

distance vs. time graph. Origin (0,0) is represented as a detector of motion. You read the statement and plot a line either near or far from the detector. After that, you follow the next step which may say what 'speed' the line should like: fast(steep line, increasing), constant(regular decreasing or increasing, a straight line), still(horizontal line), away(regular increasing), or toward the detector (regular decreasing). Be sure to read instructions and accurately display the line's directions carefully.

Points that ARE on the line

final answer would match with the equation given. EX: 10 = 10.

points that ARE NOT on the line

final answer would not match with the equation given. EX: 11 =10.

Functions

horizontal lines and negative or positive slopes. Functions can have repeated Y's.

Find the intercepts

identify where the y-intercept and x-intercept are on the graph. Write answer as points. EX: (0,2) and (-2,0).

Quadrant iii

negative, negative

Quadrant ii

negative, positive. negative #'s on the x-coordinate, positive #'s on the y-coordinate. Quadrant is on your left.

Quadrant iv

positive, negative. Quadrant is across from quadrant 2.

Quadrant i

positive, positive

Rate of Change in the real world

rate of change = change in cost/change in time. You use your x and y chart to solve. You see how the prices change between each day. Next you find the change in days. You divide the change you found for days and cost to give you a unit rate, which is quantity over 1. EX: $.10/2. divide $0.10 by 2. You get $0.05/1. (the cost for a gallon of gas is $0.05 per day).

Zero Slope

the slope of a horizontal line. It's a zero over a #. Looks like this: 0/# visualize it like 0/N. "0/N" means good since because your answer is just zero.

Undefined slope

the slope of a vertical line. Looks like this #/0. It's a Number over zero. Visualize it line N/0. "N/0" means no good since a number can't divide into zero, so your answer would be undefined.

Domain

x values, input.

Range

y values, output.

Rate of Change Algebraically

y2-y1/x2-x1