Algebra and Graphing: Key Concepts and Problem Solving

Solve and graph: y = 2x - 3

Take (0, -3) as y-intercept; slope = 2 → up 2, right 1. Plot and draw the line.

Find the slope between (2, 5) and (4, 9)

m = (9 - 5) / (4 - 2) = 4 / 2 = 2

Evaluate f(x) = -3x + 4 when x = -2

f(-2) = -3(-2) + 4 = 6 + 4 = 10

Is the relation {(1, 3), (2, 5), (1, -2)} a function?

No - input 1 has two different outputs

Solve |x - 4| = 6

x = 10 or x = -2

Solve and graph: 3x - 5 < 7

x < 4; graph open circle at 4 with arrow left

Solve and graph: |x + 2| > 5

x < -7 or x > 3; graph both with open circles, arrows left and right

Graph y = -½x + 1

Plot (0, 1); slope = down 1, right 2 → (2, 0); draw line

Evaluate f(x) = 2x² - x when x = 3

f(3) = 2(9) - 3 = 18 - 3 = 15

Solve |2x - 1| ≤ 5

-2 ≤ x ≤ 3; graph closed circle at -2 and 3 with line in between

Does a graph fail the vertical line test if a vertical line hits it twice?

Yes - it's not a function

Solve and graph: -2x + 3 ≥ 7

x ≤ -2; flip sign when dividing by negative. Graph closed circle at -2, arrow left.