📊 FUNCTIONS
Is the relation {(2, 5), (3, 6), (2, 8)} a function? Explain?
No, because the input 2 is repeated with different outputs.
What is the slope of the line that passes through (1, 2) and (3, 6)?
Slope = (6 – 2)/(3 – 1) = 4/2 = 2
M=2
Simplify: 23
8
What the graph of a quadratic function called?
A parabola
what is the solution to a system of equations.
The point of intersection between both lines.
Solve the equation:
|x|-6=4
x =±10
What is the range of the function f(x) = 3x – 2 for x = –1, 0, 1, 2?
f(x) = –5, –2, 1, 4 → Range: {–5, –2, 1, 4}
Write the equation of a line with slope 4 and y-intercept –3.
y = 4x – 3
Simplify: x3⋅ x2
x5
Find the axis of symmetry of y = x² + 4x + 3.
x = –2
What does it mean when a system has no solution?
The lines are parallel and never intersect.
Solve the equation.
4|x-5| = 12
x = 8 or x = 2
Identify the domain of the function represented by the table:
x | –2 | –1 | 0 | 1 |
y | 4 | 2 | 0 | –2
Domain: {–2, –1, 0, 1}
Convert 3x – 4y = 12 to slope-intercept form.
y = (3/4)x – 3
Simplify: (3x2)2
9x4
Factor: x2+5x+6
(x + 2)(x + 3)
Solve by substitution:
y = 2x,
3x + y = 12
Solution: (2.4, 4.8)
Solve:
4|x+3|-7=5
x = 0 or x = -6
Is the graph of y = x² a linear function? Why or why not?
No, because it is not a straight line—it is quadratic.
Find the x-intercept of the equation: y = –2x + 8
Set y = 0: 0 = –2x + 8 → x = 4
Simplify: x7 / x4
x3
Solve: x2=49
x = ±7
Solve using elimination:
2x + y = 7
3x – y = 8
(3, 1)
Solve the equation.
-3|x-1|+5=8
No Solution
The function f(x) = 2x + 1 models the cost of x movie tickets. What is the cost for 3 tickets, and what does the slope represent?
Cost = $7; slope = 2 → the cost per ticket.
A line passes through (2, 5) and has a slope of –3. Write its equation in point-slope form.
y – 5 = –3(x – 2)
Evaluate: ((2x2y3) / (4xy))2
(x2y4) / 4
Given the equation y = –x² + 6x – 5, find the vertex.
Vertex = (3, 4)
A system has infinitely many solutions. What does this mean graphically?
The two equations represent the same line.
Solve the equation.
0.8|x+4|-3=1
x = -9 or x = 1