1.1: Lines in the Plane
What kind of slope does a vertical line have?
Undefined
Is the following relation representative of a function?
f: {(-1,2), (5,3), (0,-1), (-1,4), (2,0)}
No
Is the following equation a function? Use Desmos.
x+y^2=4
No
Find the slope between the two points:
(4, 5) and (8, 4)
m= -1/4
Does Figure 1 on the board show a function?
Yes
Approximate the relative minimum and relative maximum of the function. Use Desmos.
f(x)=x^3-6x^2+15.
Relative minimum: (3,-9)
Relative Maximum: (0,15)
Write the equation of the line that goes through the points: (2, -7) and (-1, 2)
y=3x-13
Given f(x)=3-2x, find f(x+4)
f(x+4)=-2x-5
Given the function, find the open intervals for which the function is increasing, decreasing or constant. Use Desmos.
f(x)=3x^4-6x^2
Increasing: (-1, 0) U (1, inf)
Decreasing: (-inf, -1) U (0,1)
Are the following lines parallel, perpendicular, or neither?
y=3x-4
x+3y=4
Perpendicular
Use the piecewise function in Figure 2 to find f(1).
5
Find the domain and range of the function in interval notation. Use Desmos.
f(x)=sqrt(2-x)+3
Domain: (-inf,2]
Range: [3,inf)
Write the equation of the line that passes through the point (2, 1) and is parallel to the line 4x-2y=3
y=2x-3
Find the domain algebraically. Write in interval notation
f(x)=1/(x+5)
Describe the function as even, odd, or neither. Show your work algebraically.
f(x)=x^4-x^2+3
Even