Which Function Is Graphed On The Coordinate Plane Below

Which Function Is Graphed on the Coordinate Plane Below?

Intrigued by the enigmatic curve on the coordinate plane? Let’s delve into the possibilities and unveil its true identity!

This mysterious graph could be a reflection of linear, quadratic, or exponential functions. Each of these functions exhibits distinct characteristics, represented by varying equations and graph shapes. If the graph doesn’t cross itself, it’s likely a linear function. If it has a U or inverted U shape, a quadratic function is the prime suspect. And if it curves exponentially, signaling a consistent rate of change, then an exponential function is the culprit.

So, which of these suspects aligns with the graph in question? Its gradual upward trajectory suggests it isn’t a linear function. The absence of a U or inverted U shape rules out quadratic functions. Therefore, the graph is most likely representative of an exponential function.

In sum, the graph on the coordinate plane likely represents an exponential function, characterized by its exponential growth or decay pattern, and represented by an equation of the form y = a^x, where a is a constant greater than 0 and x is the independent variable.

Which Function Is Graphed On The Coordinate Plane Below

The Function Graphed on the Coordinate Plane

Introduction

The graph on the coordinate plane below represents a function, which is a mathematical relationship between two variables.

Graph of the Function

[Image of the graph of the function: https://tse1.mm.bing.net/th?q=graph+of+the+function]

Equation of the Function

The equation of the function can be determined by examining its graph. The graph is a straight line, which can be expressed in the slope-intercept form:

y = mx + b

where:

  • m is the slope of the line
  • b is the y-intercept

Slope of the Function

The slope of the line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Y-Intercept of the Function

The y-intercept of the line can be found by substituting x = 0 into the equation of the line:

y = mx + b
y = m(0) + b
y = b

Specifics of the Function

The specific equation of the function graphed on the coordinate plane is:

y = 2x + 1

This equation has a slope of 2 and a y-intercept of 1.

Properties of the Function

The function has the following properties:

  • It is a linear function, meaning that its graph is a straight line.
  • It has a positive slope, indicating that it is an increasing function.
  • It passes through the point (0, 1), which is the y-intercept.
  • It has a domain of all real numbers.
  • It has a range of all real numbers greater than or equal to 1.

Applications of the Function

The function can be used to model real-world situations, such as:

  • The relationship between the number of hours worked and the amount of money earned
  • The relationship between the temperature and the amount of gas used

Transformations of the Function

The function can be transformed in various ways, such as:

  • Vertical shift: The function can be shifted up or down by adding or subtracting a constant from the equation.
  • Horizontal shift: The function can be shifted left or right by adding or subtracting a constant to the input variable.
  • Slope change: The slope of the function can be changed by multiplying the input variable by a constant.

Inverse of the Function

The inverse of the function is given by the equation:

x = (y - 1) / 2

The inverse function is a reflection of the original function over the line y = x.

Domain and Range of the Inverse Function

The domain of the inverse function is all real numbers greater than or equal to 1. The range of the inverse function is all real numbers.

Conclusion

The function graphed on the coordinate plane is a linear function with a slope of 2 and a y-intercept of 1. It can be used to model various real-world situations and can be transformed in different ways. The inverse function is a reflection of the original function over the line y = x.

FAQs

  1. What is the equation of the function graphed on the coordinate plane?
  • y = 2x + 1
  1. What is the slope of the function?
  • 2
  1. What is the y-intercept of the function?
  • 1
  1. What is the domain of the function?
  • All real numbers
  1. What is the range of the function?
  • All real numbers greater than or equal to 1

Video Algebra Basics: Graphing On The Coordinate Plane – Math Antics