POWERS & EXPONENTS
Evaluate: 23
What is 8.
A proportional relationship has a __________ unit rate.
What is a constant unit rate
Determine whether each equation has one solution, no solution, or infinitely many solutions:
a. 4x+8=4(x+2)
b. 5x−3=2x+12
c. 7x+1=7x−5
A. Infinate Many Solutions
B. One Solution
C. No Solution
What makes a relation a function?
What is each input has exactly one output?
A graph shows a line with slope −3 and y-intercept 5.
Write the equation of the line.
What is y = −3x + 5?
What is y = −3x + 5?
Write 4x4x4 using exponents
What is 43
Does this table show a proportional relationship? Explain your answer.
X 2 4 6
_______________
Y 6 12 18
Yes because the y-intercept is 0
when 2 parallel lines are cut by a transveral, these angles are in the same relative location and they are equal
What are corresponding angles?
Tell whether the relation is a function. Explain.
{(-4, 2), (1, 1), (1, -1), (4, -2)}
What no because input 1 has more then 1 output
Function A: y = 3x
Function B (table):
X 1 2 3
Y 2 4 6
Which function has the greater rate of change?
What is Function A because its slope is 3 compared to 2?
What is greater 23 or 32
What is 32 because 9 is greater than 8
Does this table show a proportional relationship? Explain your answer.
X 0 1 2
_______________
Y 3 5 7
No it is not proportional because it has a y-intercept of 3
Solve the equation:
7−2(x−5)=3x+1
What is X=9
True or False a line with a zero slope is a function? Explain.
What is true. A line with a zero slope will be a vertical line which means each input will have only one output
Two graphs are shown.
Graph A passes through (0,0) and (2,4)
Graph B passes through (0,3) and (2,5)
Which graph has the greater rate of change?
What is Graph A because its slope is 2 compared to 1?
Evaluate (23)2
What is 64
A taxi company charges a constant rate per mile. The graph below shows the cost for miles driven:
At 1 mile: $2.75
At 3 miles: $8.25
Determine the unit rate and write an equation for cost C in terms of miles m.
What is C=2.75m
Solve the equation:
3(2x−4)=5x+6
What is X=18
What are the another two names that can be used synonymously for input
What is domain and x-value
A function is represented by the equation y=−3x+7
a. Identify the slope and y‑intercept.
b. Explain what each value means in context if the function represents money remaining on a gift card after buying items.
a. Slope: −3 y‑intercept: 7
Slope −3: For each item (or unit of x), the amount on the card decreases by 3 dollars.
Y‑intercept 7: The starting amount on the gift card is 7 dollars.
True or false 102 is equal to 10 x 2
What is False? Exponents mean repeated multiplication.
A line representing a proportional relationship has a slope of 5/3. Write two different points (other than the origin) that lie on the line.
answers will vary but possible solutions could be (3,5), (6,10), (9,15), (12,20), (15,25)
Explain how you can tell whether an equation has no solution without solving it completely. Provide an example.
If the coefficients are the same but the constants are different there will be no solution
Are all relations functions? Explain your answer.
What is No
A linear function has a y-intercept of 4 and increases by 3 for every 1 unit of x.
Question: Write the equation and explain how you know it’s a function.
What is y = 3x + 4, and it’s a function because each input has exactly one output?