- The graph of cf(dx) is the graph of f(x) stretched vertically by a factor of c for c>1 (or compressed by a factor of c if 0<c<1) and stretched horizontally by a factor of 1d for 0<d<1 (or compressed by a factor of 1d if d>1)
- A real number r is a root or zero of the polynomial function f if f(r)≠0
- The Rational Root Test tells us that every rational root of f can be written as r=pq, where p and q are integers with no common factors other than 1, and p is a factor of the constant term a0 and q is a factor of the leading coefficient an
- For any real number, X, an exponential is a function with the form f(x)=ab^x where a is a ________ ______ number called the ________ value and b is any _______ ________ number such that b does not equal 1
- Look out for ______ in graphs when solving for the domain and range
- f(x)=ln(x) is called the natural logarithmic function
- f(x)=ex is called the natural exponential function.
- The drama club sold a total of 360 adult and student tickets for the school play. Charging $5 for each adult ticket and $3 for each student ticket, they collected $1,360 from ticket sales. How many student tickets did the drama club sell?
- Solving equations involving logarithms can introduce extraneous solutions, so it is important to verify the solutions
- Exponential decay, f(x)=ab^x where A is the ________ value of the function, b is the ______ factor, and r is the decay rate
- The graph of y=log(x) is the graph of y=10x reflected about the y-axis
- Identity Function/ Linear Parent Function
- The base a logarithm of a positive number x is the exponent in the power of a that has x as its value
- Exponential growth, f(x)= ab^x where A is the _______ value of the function, B is the ________ ______ and b is greater than ____
- For a>1, as x increases, f(x)=ax increases faster than the linear function g(x)=x and slower than the quadratic function h(x)=x^2.
- An exponential function has the form of a constant raised to a variable power: f(x)=ax, where a is a positive real number not equal to 1.
- The function f(x)=b^x is only an exponential function for certain values of b. What are the values of b that are allowed?
- A system of equations and its solution are given below.System Ax - y = 3-2x + 4y = -2Solution: (5, 2)Complete the sentences to explain what steps were followed to obtain the system of equations below.System Bx - y = 32x = 10To get system B, the_______________ equation in system A was replaced by the sum of that equation and the_______________equation multiplied by___________. The solution to system B_______________the same as the solution to system A.
- The exponential function f(x)=ax has domain D=(−∞,∞) and range [0, ∞)
- Evaluate the following expression when x = -4 and y = 4.x^6 - x / 4y