1. Linear Equations in Two Variables & Functions
Pre-Calculus

2. SLOPE Slope is defined in three ways… 1) 2) 3)
A line with a ______________ slope rises from left to right.
A line with a _______________ slope falls from left to right.

3. FIND THE SLOPE
(-3, 2) (5, 12)
(8, 3) (-2, -9)

4. SPECIAL SLOPES A ___________ line has a zero slope
A ___________ line has an undefined slope

5. Parallel & Perpendicular Lines
Two lines are ______________ if their slopes are equal
Two lines are ______________ if their slopes are opposite reciprocals

6. Are the two lines parallel or perpendicular?
Line A: (-3, 2) (4, -7)
Line B: (9, 7) (2, 16)
Line A (4, -8) (4, 2)
Line B (-3, -8) (8, -8)

7. SLOPE INTERCEPT FORM y = mx + b y-int slope
A line that is written in the linear form, y = mx + b is in slope-intercept form. You can graph these lines by plotting the y- intercept and using the slope to define a second point on the line.

8. GRAPH!
y = ½x – 3
6x – 3y = 12

9. POINT SLOPE FORM
An additional form of a linear equation is called the point-slope form. The equation of a line with a slope, m and passing through (x1, y1) is
y – y1 = m(x – x1)

10. FIND THE SLOPE INTERCEPT FORM OF EACH LINE--
(-1, 3) m = ½ (-5, 9) m = undef. (5, -1) (3, 7)

11. Find the slope-intercept form of the equation passing through (2, -1) and perpendicular to the line 2x – 3y = 5

12. A kitchen appliance manufacturing company determines that the total cost in dollars of producing x units of a blender is
C = 25x
Describe the practical significance of the y- intercept and slope of this line.

13. FUNCTIONS
A function is a relation in which each element of the domain is paired with exactly one element of the range…
____________ do not repeat!
DOMAIN
RANGE

14. 4 WAYS TO REPRESENT A FUNCTION:
VERBALLY
NUMERICALLY
GRAPHICALLY
ALGEBRAICALLY

15. ARE THESE FUNCTIONS?

16. FUNCTIONAL NOTATION f(x) is read as “f of x”
y is a __________________________
can be named ___________________
for f(x) ________________________

17. f(w) = 4w3 – 5w2 – 7w + 13
f(-2)
f(3)
f(x)

18. PIECE-WISE FUNCTION
A piece-wise function is defined by 2 or more equations over a specified domain.

19. 𝑦= 𝑥 2 +1, x<0 𝑥−1, 𝑥≥0
GRAPH IT!
f(-1)
f(0)
f(1)

20. f(x) = 2, 𝑥<−2 𝑥 2 −1, 𝑥≥ −2
Graph it!
f(0)
f(-2)
f(-3)

21. 𝑦= −𝑥 2 +2, x>−1 𝑥+1, 𝑥≤−1 On calculator…. Look at table! f(-2)

22. FINDING THE DOMAIN OF A FUNCTION
The implied domain of a function is the set of all real numbers for which the expression is defined. You must exclude x values that result in division by zero or even roots of negative numbers….
[you cannot divide by zero nor take the
square root of negative #]

23. FIND THE DOMAIN…
y= x2 + 3x + 2
f(x) = 5𝑥−8
f(x) = 1 𝑥 2 −4

24. IN CONCLUSION…
*When finding the domain you only have to worry about two special cases!!!
Everything else is ALL REAL NUMBERS!
Try this one :0)
f(t) = 𝑡−1 𝑡−4