WARMUPSolve for x5

Solve for x and show your answer in graphical and set notation

Solve for b:

• REVIEW

Evaluate the Expression

What is the property of real numbers that describes the following equality?

Write an algebraic expression for the following sentence:

You have ten dollars on Monday and spend 2 dollars every day on candy bars

Simplify by combining like items:

• Notes:Quiz NEXTTest FridayPRETEST next Tuesday – SOL rules, leave things in locker, please

Linear Functions

• lin·e·ar [ˈlinēər] - ADJECTIVE1. arranged in or extending along a straight or nearly straight line: "linear arrangements“; synonyms: straight · direct · undeviating · as straight as an arrow · [more] sequential2. consisting of or predominantly formed using lines or outlines: "simple linear designs"3. involving one dimension only: "linear elasticity"4. able to be represented by a straight line on a graph; involving or exhibiting directly proportional change in two related quantities: "linear functions"5. progressing from one stage to another in a single series of steps; sequential: "a linear narrative"

Parent function

DOMAIN (start “walking” the x-axis from left to right. Look up and down and look if you see the “line”. Write down the interval of x-axis where you find the line

________________RANGE (start “walking” the x-axis from left to right. Look up and down and look if you see the “line”. Write down the interval of x-axis where you find the line)

__________________x-INTERCEPT (calculate the x value where f(x)=0, or y=0)

____________________y-INTERCEPT (substitute x=0) into the function equation)

____________________

• Parent function (continued)

INTERVAL of INCREASE/DECREASE (start walking the x-axis from left to right, and follow the graph with your eye. Is it going up or down? What are the x values where it is going up? What are the x values where it is going down?)

____________________

END BEHAVIOR

TRANSFORMATIONSGraph the following functions and explain how they appear in comparison to the parent function (

_________________ ______________________ __________________

____________________ ______________________ ___________________

VOCABULARY:SHIFT (up or down) – TRANSLATIONSTEEPER/FLATTER – STRETCH/SHRINKFLIP over the x- Axis – REFLECTION over the x-axis

SLOPE – Rise/Run = Change in vertical direction/change in horizontal direction

BONUS: Slope of parallel lines are equal( are all parallel)Slope of perpendicular lines are negative reciprocals ( are perpendicular)are perpendicular)

𝑎𝑥+𝑏

a=SLOPEa>1 STRETCHa<1 SHRINK

b=y-interceptb>0 TRANSLATION UPB<0 TRANSLATION DOWN

DESCRIBE:

Domain: _______Range: ______Slope:X-intercept: ________Y-intercept: _______Interval of Increase: ________Interval of Decrease: ________End Behavior:

CALCULATE SLOPE:WHAT IS THE SLOPE OF THE LINE crossing points (-2,5) and (3,5)

SLOPE=RISE/RUN=

CALCULATE SLOPE AND DESCRIBE the line that goes through points (3, 4) and (-5,12). What is the slope of the line?

What is the y intercept of the line?

What is the equation of the line?

What is the equation of a parallel line?

What is the equation of a perpendicular line?

DESCRIBE:

Domain: _______Range: ______Slope:X-intercept: ________Y-intercept: _______Interval of Increase: ________Interval of Decrease: ________End Behavior:

What are the transformations of the parent function to arrive at the function above?What is the domain of this function?What is the range of this function?What is the x-intercept of this function?What is the y intercept of this function?What is the interval of increase/decrease of this function?What are the end behavior of this function?Write a function equation of a parallel line:Write a function equation of a perpendicular line