What is the definition of a function? โ A rule that assigns each input exactly one output.A function maps each element of the domain to exactly one element of the range โ one input, one output.
Which ordered pair could be added to {(1,2),(3,4),(5,6)} without destroying the function? โ (7, 2).(7, 2) introduces a new x-value (7), keeping each input paired with exactly one output. The others repeat x-values already in the set.
Using the vertical line test: if any vertical line crosses a graph at 2 or more points, the graph represents: โ Not a function.The vertical line test checks whether each x-value (vertical line) maps to more than one y-value. If so, it is not a function.
Which of these is the domain of a function? โ The set of all allowable input values (x-values).The domain is the set of all valid inputs for a function.
Which of these is the range of a function? โ The set of all output values (y-values).The range is the set of all values produced as outputs.
Does the table x: 1,2,3,2 | y: 5,6,7,8 represent a function? โ No โ x=2 maps to both 6 and 8.x = 2 appears twice with different y-values (6 and 8), violating the one-output-per-input rule.
Can two different inputs share the same output in a function? โ Yes โ multiple inputs can map to the same output.Functions allow many-to-one mappings (multiple inputs โ same output). What is forbidden is one input โ multiple outputs.
The function f is defined by f(x) = xยฒ. What is f(โ3)? โ 9.f(โ3) = (โ3)ยฒ = 9. Squaring a negative number gives a positive result.
Which notation represents the output of a function f at input x = 7? โ f(7).Function notation f(7) means "evaluate f at x = 7." It is read "f of 7."
What is the output when input 0 is used in f(x) = 5x โ 3? โ โ3.f(0) = 5(0) โ 3 = โ3.
The graph of y = x (diagonal line through origin) โ does it represent a function? โ Yes โ each x-value maps to exactly one y-value.A straight line that is not vertical passes the vertical line test. y = x maps every x to exactly one y.
Given f(x) = 6, what is f(100)? โ 6.f(x) = 6 is a constant function โ every input gives output 6.
Which representation gives the y-intercept most directly? โ Equation in slope-intercept form y = mx + b.In y = mx + b, b is the y-intercept โ you can read it directly from the equation.
A linear function's graph is: โ A straight line.A linear function has a constant rate of change, and its graph is always a straight line.
Which equation represents a linear function? โ y = 3x + 2.y = 3x + 2 is in the form y = mx + b with constant slope 3. The others are nonlinear (quadratic, exponential, cubic).
Which equation represents a nonlinear function? โ y = xยฒ.y = xยฒ is quadratic โ its graph is a parabola, which curves. All others are linear.
In a table, x increases by 1 each time. For a linear function, y should: โ Increase by the same amount each time.Linear functions have constant rate of change. For equal x-steps, y changes by the same amount each time.
A table shows: x = 0, 1, 2, 3 and y = 2, 4, 6, 8. Is this linear or nonlinear? โ Linear โ y increases by 2 each time.ฮy = 2 consistently for every unit increase in x. Constant rate of change = linear.
A table shows: x = 0, 1, 2, 3 and y = 1, 2, 4, 8. Is this linear or nonlinear? โ Nonlinear โ y doubles each time (exponential).ฮy: 1, 2, 4 โ not constant. This is exponential (y = 2หฃ), which is nonlinear.
A nonlinear function's rate of change is: โ Varying (not constant).The defining characteristic of a nonlinear function is that its rate of change varies โ it is not constant between different intervals.
On a graph, how can you quickly tell if a function is nonlinear? โ The graph is not a straight line (it curves).Any graph that is not a perfectly straight line represents a nonlinear function. Look for curves, parabolas, or exponential shapes.