Function Junction
This is what you plug into a function to get at an output.
What is the input (or x-value)?
This is the point where a graph crosses the y-axis.
What is the y-intercept?
This is the standard form of a linear equation.
What is y=mx+b?
This is what you set a function equal to when solving for the x-intercepts.
What is 0?
Simplify: i² + 3
What is 2?
(Since i² = –1 → –1 + 3 = 2)
If f(4) = 10, then 4 is the input and 10 is this.
What is the output (or f(x))?
The graph of an absolute value function has a V shape. This point at the bottom (or top) of the V tells you where the graph changes direction.
What is the vertex?
Factored form of a quadratic helps you find these key graph features.
What are the x-intercepts (or roots/zeros)?
The x-intercepts of a graph are also called these two other names.
What are zeros and roots?
Factor: x² – 9x
What is x(x – 9)?
This is the set that contains all possible inputs that a function can take.
What is the domain?
This is the effect of adding 5 outside the function: f(x) + 5
What is a vertical shift up 5 units?
This form of a quadratic equation makes it easy to graph the vertex.
What is vertex form (y=a(x–h)²+k)?
You can find the y-intercept of any function by plugging in this value for x.
What is 0?
Solve by factoring: x² – 7x + 12 = 0
What is x = 3 and x = 4?
What is the vertical line test?
This transformation moves the graph of f(x) = x2 to the right 4 units.
What is f(x) = (x-4)2?
This is why rational expressions can't have variables in the denominator equal to certain values.
What is division by zero is undefined?
This is how many x-intercepts a quadratic can have.
What is 0, 1, or 2?
This is the exponential form of log₂(32).
What is 5?
(Since 2⁵ = 32)
If
f(x) = 3x+2 and g(x) = x^2
Then this is what (f (g(x)) equals.
What is
f(g(x)) = 3x^2 +2
If the graph of a function reflects over the x-axis, this means this was done to the function.
What is multiplying the function by -1 (e.g., -f(x))?
This equation represents exponential decay: y = a(b)x — but only if this condition is true.
What is the exponent is negative, or the base b is a fraction between 0 and 1?
The type of number you get when you take the square root of a negative number.
What is a complex number?
Solve for x:
2log₃(x) = 4
What is x = 9?
Divide both sides by 2 → log₃(x) = 2 → x = 3² = 9
This is the test a graph must pass to have an inverse.
What is the horizontal line test (or 1:1 test)?
What is the line y=x?
This function is the inverse of the function y=bx.
What is logb(x) = y?
When a quadratic touches the x-axis only once, it means this about the solution.
What is there is one real repeated root (a double root)?
These are the vertical asymptotes of the function:
f(x) = 1/(x^2-5x+6)
What are x=2, and x=3?