Function Notation and Linear Functions
Function notation and linear functions are foundational concepts in mathematics, particularly in the study of algebra and calculus. Function notation provides a concise way to represent mathematical relationships between variables, while linear functions describe relationships that can be graphically represented as straight lines. Understanding function notation and linear functions is crucial for solving equations, analyzing data, and making predictions in various fields such as economics, physics, and engineering. In this introduction, we will explore the principles of function notation and delve into the characteristics and applications of linear functions.
Questions
- How do you evaluate #f(x+1)# given the function #f(x)=3-\frac{1}{2} x#?
- What is the function that describes this sequence: 4, 9, 16, …?
- Show that the function #f(x)=4x^2-5x# has a zero between #1# and #2#.
- Use a mapping diagram to determine whether the relation is a function. {(4,5), (1,8), (1,9), (9,6), (2,13), (4,1)} Which of the following mapping diagrams represents the relation?
- How do you solve the equation for y, given #y+7x=9# then find the value for each value of x: -1, 0, 4?
- How do you find the ordered-pair solution of #y=(2/5)x+2# corresponding to x= -5?
- How do you rewrite #9x+3y=6# in function notation?
- How do you write linear equations in function notation?
- Is #y=5-4x# a linear equation?
- Is #x/2 - y = 7# a linear equation?
- Is #Ax+B=C# a linear equation?
- What is an example of a linear equation written in function notation?
- How do you use function notation to write the equation of the line with the slope of 2 and y-intercept of #(0,-6/7)#?
- How do you evaluate #g(-1)# given the function #g(t)=-5t+1#?
- Let f(x) = 2- x^2 and g(x) = x^2 -2. How do you solve f(x) = g(x) ?
- Is #y= 12+2x# a linear equation?
- How do you find three different ordered pairs #y=2x+1#?
- What kind of a function is #f (x) = -2x + 6 #?
- How do you determine whether or not the point (3,2) are solutions of #2x+3y=12#?
- Is #y=2+5x^2# a linear equation?