Which graph represents a function? โ A straight line crossing the graph once per vertical line.A straight line, vertical line test: any vertical line crosses it exactly once. A circle, sideways parabola, or ellipse would be crossed twice in some places.
If f(x) = 2x + 5, what value of x gives f(x) = 13? โ x = 4.2x + 5 = 13 โ 2x = 8 โ x = 4.
A vending machine takes a dollar code and gives one snack. Is this a function? โ Yes โ each code (input) gives exactly one snack (output).Each valid input (code) maps to exactly one output (snack type). This is a real-world function.
Is y = xยฒ a function? โ Yes โ each x-value produces exactly one y-value.For each x input, xยฒ gives exactly one output. (โ3 and 3 give the same output 9, but that does not disqualify it as a function.)
Is x = 4 (a vertical line) a function of x? โ No โ x = 4 gives infinitely many y-values for one x.A vertical line fails the vertical line test: x = 4 maps the single input x = 4 to all real y-values โ not a function.
A student claims: "If a graph passes the horizontal line test, it is a function." Is this correct? โ No โ functions require the vertical line test.The vertical line test determines if a graph is a function. The horizontal line test determines if a function is one-to-one.
Which mapping represents a function from set A = {1,2,3} to set B = {4,5,6}? โ 1โ4, 2โ5, 3โ5.Only the first mapping assigns each element of A to exactly one element of B. The others map some input to two outputs.
In a function machine, input 5 โ output 17 and input 3 โ output 11. What rule could this be? โ f(x) = 3x + 2.Check f(5) = 3(5)+2 = 17 โ and f(3) = 3(3)+2 = 11 โ. The rule is f(x) = 3x + 2.
Is the relationship "each student in a class โ their birthday" a function? โ Yes โ each student has exactly one birthday.Each student (input) has exactly one birthday (output). Sharing birthdays is allowed โ multiple inputs can share an output.
A table has columns x and y. If every x-value in the table is different, is it guaranteed to be a function? โ Yes โ unique x-values ensure each input has one output.With each x appearing only once, every input maps to at most one output. This is sufficient to be a function.
For f(x) = |x| (absolute value), what is f(โ7)? โ 7.|โ7| = 7. The absolute value function always returns a non-negative output.
Function A: y = 5x + 2. Function B: passes through (0, 4) and (1, 7). Which has a greater slope? โ Function A (slope 5 > B slope 3).Function B slope = (7โ4)/(1โ0) = 3. Function A slope = 5. Function A has the greater slope.
Function C: y = 2x โ 3. Function D table: x: 0,1,2 | y: 1,4,7. Which has the greater y-intercept? โ Function D (b=1 > b=โ3).Function C: b = โ3. Function D: at x=0, y=1 so b=1. Since 1 > โ3, Function D has the greater y-intercept.
f(x) = โ2x + 10. For what x does f(x) = 0? โ x = 5.โ2x + 10 = 0 โ โ2x = โ10 โ x = 5.
Two functions: f(x) = x + 3 and g(x) = 2x + 1. For what value of x are they equal? โ x = 2.x + 3 = 2x + 1 โ 2 = x. So x = 2.
A table shows: x: โ1, 0, 1, 2 and f(x): โ1, 3, 7, 11. What is the rate of change? โ 4.Differences: 3โ(โ1) = 4, 7โ3 = 4, 11โ7 = 4. The constant difference is 4 per unit of x.
f(x) = 3x โ 1. Which ordered pair lies on this function? โ (2, 5).f(2) = 3(2) โ 1 = 5. So (2, 5) lies on the graph.
If f(3) = 10 and f(6) = 19, what is the rate of change (assuming linear)? โ 3.Rate of change = (19 โ 10)/(6 โ 3) = 9/3 = 3.
Given f(x) = |2x โ 4|, what is f(1)? โ 2.f(1) = |2(1) โ 4| = |2 โ 4| = |โ2| = 2.
f(x) = 2x + 4 is represented by the table x: 0,1,2,3 | y: 4,6,8,10. What is f(10)? โ 24.f(10) = 2(10) + 4 = 24.
Which function has the greater value at x = 3: f(x) = 2x + 1 or g(x) = x + 5? โ f(3) = 7 = g(3) = 8, so g is greater.f(3) = 2(3)+1 = 7. g(3) = 3+5 = 8. g(3) > f(3), so g is greater at x=3.
A function f is shown in a graph as a straight line passing through (0, 2) and (3, 8). What is the equation? โ f(x) = 2x + 2.Slope = (8โ2)/(3โ0) = 2. y-intercept = 2. Equation: f(x) = 2x + 2.
Find the input x if f(x) = 0 for f(x) = โ5x + 20. โ x = 4.โ5x + 20 = 0 โ 5x = 20 โ x = 4. This is the x-intercept (zero) of the function.
Which pair of functions has the same y-intercept? โ f(x) = 5x + 3 and g(x) = โ2x + 3.Both f(x) = 5x + 3 and g(x) = โ2x + 3 have b = 3. The others have different y-intercepts.
What is the key feature that makes a function LINEAR? โ The rate of change (slope) is constant.The defining feature of a linear function is its constant rate of change (slope). Equal changes in x produce equal changes in y.
Which graph feature indicates a nonlinear function? โ A curve (parabola or exponential).Any curve โ whether a parabola, S-curve, or exponential โ indicates a nonlinear function. Linear functions only appear as straight lines.
The equation y = 4 represents which type of function? โ Linear โ a horizontal line (slope = 0).y = 4 is a horizontal line with slope 0. It is still a linear function (a special case with zero slope).
Table: x = 1, 2, 3, 4 and y = 3, 5, 7, 9. What is the rate of change? โ 2.ฮy = 2 for each ฮx = 1. Rate of change (slope) = 2.
A linear function passes through (0, 3) and (2, 9). What is its slope? โ 3.Slope = ฮy/ฮx = (9โ3)/(2โ0) = 6/2 = 3.
Which of these tables represents a nonlinear function? (x increases by 1 each time) โ y: 1, 4, 9, 16 (ฮy: 3, 5, 7).y: 1, 4, 9, 16 โ differences are 3, 5, 7 (increasing). Not constant โ nonlinear (y = xยฒ).
y = โ3x + 1 and y = xยฒ โ 2. Which is linear? โ Only y = โ3x + 1.y = โ3x + 1 is linear (slope = โ3, y-intercept = 1). y = xยฒ โ 2 is quadratic (nonlinear).
Which data set does NOT represent a linear function? โ (1,2), (2,4), (3,8), (4,16).(1,2),(2,4),(3,8),(4,16) โ y doubles each time. Differences: 2, 4, 8 (not constant). This is exponential, not linear.
y = 3xยฒ + x โ 5 represents which type of function? โ Quadratic (nonlinear).The xยฒ term makes this a quadratic (degree 2) polynomial โ it is nonlinear. Its graph is a parabola.
A function's table shows first differences that are constant. What does this tell you? โ The function is linear.Constant first differences (ฮy) for constant ฮx is the hallmark of a linear function.