Algebra Review: Slopes, Functions, Circles, and Intercepts (Video Notes)

A set of practice flashcards covering slope, functions, circles, lines, symmetry, domains, and intercepts from the video notes.

What is the slope of the line parallel to -3x+5y=12?

3/5

What is the equation of the horizontal line passing through the point (210, -451)?

y = -451

True or False: The relation {(-3, 7), (2, 7), (3, 7), (6, 8), (10, 4)} represents y as a function of x.

True

True or False: The equation x = y²+1 represents y as a function of x.

False

True or False: The graph of the equation y² = x² + 1 is symmetric about the origin.

True

What is the domain of the following function: f(x)=3x² +4x-10?

All real numbers (-∞, ∞)

What is the center of a circle whose equation is (x+ 600)²+(y-81)² = 89?

(-600, 81)

What is the radius of a circle whose equation is (x+600)²+(y-81)²=89?

√89

For f(x) = 3x²-6, compute the difference quotient [f(x+h) - f(x)]/h.

6x + 3h (h ≠ 0)

Find all values of x such that f(x)=0 for f(x)=3x²-6.

x = ±√2

Solve √(x² - x - 8) = x + 5. (Assuming the equation is sqrt(x^2 - x - 8) = x + 5)

x = -3 (valid because x ≥ 3; check: sqrt(9+3-8)=2 and x+5=2)

Given h(x) = 4, what is h(-2)?

4

Given h(x) = 4, what is h(1)?

4

What is the domain of h(x) if h(x) ≡ 4 for all x?

All real numbers (-∞, ∞)

Complete the square to write 2x² + 2y² -12x + 8y -24 = 0 in standard form.

(x-3)² + (y+2)² = 25

What is the center of the circle (x-3)² + (y+2)² = 25?

(3, -2)

What is the radius of the circle (x-3)² + (y+2)² = 25?

5

What are the intercepts of the circle (x-3)² + (y+2)² = 25?

x-intercepts: (3 ± √21, 0); y-intercepts: (0, 2) and (0, -6)

Find the equation of the line through (-3, 4) and (5, -2) in slope-intercept form.

y = (-3/4)x + 7/4

Is the graph of y = x² + 41 symmetric about the y-axis?

Yes (symmetric about the y-axis)

Is the graph of y = x² + 41 symmetric about the x-axis?

No

Is the graph of y = x² + 41 symmetric about the origin?

No

What is the domain of the relation { (1,2), (3,4), (5,6), (100,30), (250,6) }?

{1, 3, 5, 100, 250}

What is the domain of f(x) = (3x+5x-1)/(x-4)²?

All real numbers except x = 4

Solve (2x+3)-9=0.

x = 3

Solve 3 + sqrt(3x+1) = x.

x = 8 (note: x = 1 is extraneous)

Find the y-intercept of y = -x² - 8.

(0, -8)