A function assigns exactly ___ output(s) to each input. — One.By definition, a function assigns exactly one output to each input.
The domain of a function is: — The set of all inputs.Domain = all valid inputs (x-values). Range = all outputs (y-values).
The range of a function is: — The set of all outputs.Range = set of all possible outputs (y-values) when the domain values are substituted.
If f(x) = 5x + 1, what is f(2)? — 11.f(2) = 5(2) + 1 = 10 + 1 = 11.
Which test determines if a graph represents a function? — Vertical Line Test.Vertical Line Test: if any vertical line crosses the graph more than once, it is NOT a function.
f(x) notation means: — f of x (function named f evaluated at x).f(x) reads "f of x" and means: apply the rule f to the input x.
What is the domain of f(x) = √x? — x ≥ 0.You can take √0 (= 0) but not √(negative). Domain: x ≥ 0.
What is f(0) for f(x) = 3x² − 2x + 7? — 7.f(0) = 0 − 0 + 7 = 7. f(0) always gives the constant term.
In y = mx + b, m represents: — The slope.In slope-intercept form y = mx + b, m is the slope and b is the y-intercept.
What is the slope of y = 3x − 5? — 3.In y = 3x − 5, the coefficient of x is 3, so slope = 3.
What is the y-intercept of y = −2x + 7? — 7.y-intercept is b = 7 (the constant term).
A line with slope 0 is: — Horizontal.Slope 0 means no rise over run — the line is perfectly horizontal.
The slope formula is: — m = (y₂−y₁)/(x₂−x₁).m = rise/run = Δy/Δx = (y₂−y₁)/(x₂−x₁).
Find the slope of a line through (2, 3) and (6, 7). — 1.m = (7−3)/(6−2) = 4/4 = 1.
Two lines with the same slope are: — Parallel (or identical).Same slope → parallel lines (or the same line if y-intercepts also match).
A linear function grows by a constant ___ per step. — Amount (difference).Linear: constant first differences. Each step adds the same amount.
The first differences of a quadratic function are: — Increasing linearly.Quadratic: first differences are NOT constant, but second differences are. First differences increase linearly.
Exponential growth multiplies by a constant factor each step. If f(0)=3 and ratio=2, what is f(3)? — 24.f(3) = 3 × 2³ = 3 × 8 = 24.
Which grows fastest for very large x? — Exponential y = 2ˣ.For large x, exponential (2ˣ) eventually outpaces any polynomial, including quadratic.
A table shows: x=0,1,2,3; y=4,12,36,108. What type is this? — Exponential.Ratios: 12/4=3, 36/12=3, 108/36=3. Constant ratio = exponential: y = 4 · 3ˣ.
The graph of a quadratic function is: — A parabola.Quadratic functions y = ax² + bx + c always graph as parabolas.
Which function has a constant rate of change? — y = 5x − 2.Linear functions have constant rate of change (constant slope). y = 5x − 2 has slope 5 everywhere.
In direct variation y = kx, k is called the: — Constant of variation.k is the constant of variation (also called constant of proportionality).
In direct variation, as x increases, y: — Increases proportionally.Direct variation y = kx (k > 0): as x increases, y increases by the same factor.
If y varies directly with x, which equation fits? — y = kx.Direct variation: y = kx (y is directly proportional to x).
If y varies inversely with x, which equation fits? — y = k/x.Inverse variation: y = k/x, or equivalently xy = k (constant product).
Find k if y varies directly with x and y = 15 when x = 3. — k = 5.k = y/x = 15/3 = 5.
In inverse variation y = k/x, as x doubles, y: — Halves.If x → 2x, then y = k/(2x) = (1/2)(k/x). So y halves.
A direct variation graph passes through which special point? — The origin (0, 0).y = kx: when x = 0, y = 0. Direct variation always passes through the origin.