Transformations
What transformation has occurred? (Slide 2)
90 degree counterclockwise.
Which is not a function. (Slide 7)
First one.
It fails the vertical line test.
Where do we see the initial value it on a graph? In an equation? And on a table? (Must get all correct in order to get 100 points)
Graph = y-intercept/value where it crosses the y-axis
Equation = +/- b
Table = value of y when x is zero
Gabby is comparing 2 pet stores. The total cost, y, for each pet shops hair cut includes a one time sign up fee and an additional fee per hour of the haircut. Petshop A's cost is : y=20x+150 and Petshop B's cost is y=50x+100. Which pet shop charges more per hour? How much do they charge per hour?
Petshop B. They charge $50 an hour.
2x+6 = 3x - 10
X = 16
A dilation with a scale factor of 1/2 will be bigger or small than the pre-image? How would we find the coordinate points for our image? (Must have answer to both questions correct to earn 200 points)
Smaller.
Multiply x and y coordinate by 1/2 or divide them by 2.
Which is not a function? (Slide 8)
The second because -2 is a repeated input with a different output.
What is the initial value for this table? (Slide 11)
2
Marcus owns his own barber shop. He charges a flat rate of $50 for every haircut plus an additional $20 per treatment a customer purchases.
Josh owns a barber shop as well. He charges a flat rate of $100 plus $10 per treatment.
Which barber shop is cheaper?
Marcus= y=20x+50
Josh = y=10X+100
Marcus' shop is cheaper.
4(x-3) = 4x + 2x - 2
X = 5
What transformation has occurred? Include all necessary details. (Slide 3)
Reflection across the line x=1
Which is a linear function?
H =1/2x+4
4x^2 + 2y = 10
A = r^2+5
y=1/x+4First One.
It can't have an exponent attached to the variable nor can the variable be a denominator.
What is the initial value and the ROC for this equation?
y = 2/3x - 6
Initial value = -6
ROC = 2/3
GLA is looking for a new food service. Company A's cost is represented in the table. Company B's cost can be represented by the equation y=8X+300.
Which company has a higher initial fee? Which company charges more per plate?
Slide (14)
Initial Fee: Company B
Per Plate Cost: Company A. $83 difference.
1/3(6x+9) = 1/2 (10x+2)
x = 2/3
What series of transformations has occurred? (Slide 4)
Translation of up 2 then a rotation of 90 degree clockwise
Which is a linear function? (Slide 9)
Bottom Right.
Constant Rate of Change.
What is the ROC and initial value of this graph? Bonus 200 if you can write the equation for this graph.
ROC= -2/3
IV= 5
Equation= y=-2/3x+5
Chivala charges $75 for each cake and then an additional $6 for each decoration included on the cake.
1/3(2x+7)=2x-1
x = 10/4
x= 2 1/2
What series of transformations occurred? (Slide 5)
Reflection across x-axis then a translation of 6 to the right.
Which is a nonlinear equation?
y=2x+b
2y +4x = 10
y = 4x + 5^2
y = 5x^2 + 4
Last one.
What is the ROC and Initial Value? Bonus 100 if you can write the equation! (Slide 13)
ROC = 3
IV = -1
Equation = y=3x-1
Aliyah opens a lemonade stand. The cost or her lemonade is represented by y=.50x+2, where x is the number of ice cubes and b is the flat rate for each cup.
Trevior then opens a lemonade stand across the street and his costs are represented by the graph.
Who has a higher flat rate for a cup? Who charges more per ice cube? Who has a cheaper lemonade stand?
Aliyah charges a higher flat rate.
Trevior charges more per ice cube.
Trevior has a cheaper lemonade stand.
.5(5x+10) = .25(8x + 16)
x = -2