Algebra Questions
Explore questions in the Algebra category that you can ask Spark.E!
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