1/25
Looks like no tags are added yet.
Name | Mastery | Learn | Test | Matching | Spaced |
---|
No study sessions yet.
y = x
Linear function represented by a straight diagonal line through the origin.
y = |x|
Absolute Value function, shaped like a V with vertex at (0,0).
y = x²
Quadratic function, represented by a U-shaped parabola opening upwards.
y = x³
Cubic function, an S-curve passing through the origin, increasing in both directions.
y = x⁴
Quartic function, resembling a tighter U than the quadratic function, symmetric.
y = x⁵
Quintic function, an S-curve that is steeper than the cubic function.
y = √x
Square Root function, starts at (0,0) curving right and upwards.
y = ∛x
Cube Root function, an S-curve sideways through the origin.
y = 1/x
Rational function consisting of two curves in opposite quadrants and having vertical and horizontal asymptotes.
y = b^x
Exponential Growth function characterized by a horizontal asymptote at y = 0 and an increasing curve.
y = (1/b)^x
Exponential Decay function, showing a decreasing curve with a horizontal asymptote at y = 0.
y = log_b(x)
Logarithmic Growth function, featuring a vertical asymptote at x = 0 and a slow increase to the right.
y = log_{1/b}(x)
Logarithmic Decay function, which decreases to the right and has a vertical asymptote at x = 0.
Vertex of Absolute Value and Quadratic
For y = |x| and y = x², the vertex is at (h, k).
Inflection point for Cubic and Cube Root Functions
The inflection point or center of rotation is observed in y = x³ and y = ∛x.
Asymptotes in Exponential, Rational, Logarithmic functions
Exponential, Rational, and Logarithmic functions have asymptotes that are not points.
Only 1 y-intercept behavior
Linear, Quadratic, Absolute Value, Exponential, and Logarithmic functions always have one y-intercept.
No x-intercepts condition
Exponential function may have none; Rational function depends on asymptotes.
Domain of all real numbers
Linear, Cubic, Cube Root, Exponential, and Logarithmic functions have a domain of all real numbers.
Range behavior for Linear, Cubic, Cube Root, Logarithmic
The range is all real numbers for Linear, Cubic, Cube Root, and Logarithmic functions.
Finding solutions for Absolute Value
To solve absolute value equations, isolate the absolute value and split into two equations.
Rational function solution approach
For rational functions, find common denominators, cross-multiply, and check for extraneous solutions.
Find the number of extraneous solutions
Extraneous solutions are found in Rational, Square Root, and Logarithmic functions due to their restricted domains.
Imaginary solutions in Quadratics
Quadratics yield imaginary solutions when the discriminant is negative.
Conditions for exactly one real solution
Linear functions have exactly one real solution.
No solution scenarios
No solutions occur when the absolute value is set to a negative number or in logarithmic functions with negative inputs.