Which Function Is Graphed on the Coordinate Plane?

AvatarByDale Richard Airplane Travel Tips And Etiquettes (Do's/Don'ts)

Which Function Is Graphed On The Coordinate Plane Below?

Have you ever looked at a graph and wondered what function it represents? Or maybe you’ve been asked to identify a function from its graph. If so, then you’re in luck! This article will teach you everything you need to know about graphing functions. We’ll start by discussing the different types of functions and how they’re represented on a graph. Then, we’ll take a look at some specific examples of functions and how to identify them. By the end of this article, you’ll be able to confidently identify any function from its graph.

So let’s get started!

Which Function Is Graphed On The Coordinate Plane Below? Equation Graph
Linear Function y = mx + b
Quadratic Function y = ax^2 + bx + c
Cubic Function y = ax^3 + bx^2 + cx + d

In this tutorial, we will examine the graph of the function $y=f(x)$ shown below. We will identify the domain and range of the function, determine the intervals where the function is increasing, decreasing, and constant, find the x-intercepts and y-intercepts of the function, and determine the symmetry of the function. We will then examine the graph using algebra to write an equation for the function, find the derivative of the function, find the critical points of the function, find the inflection points of the function, and sketch the graph of the function.

Examining the Graph

Domain and Range

The domain of a function is the set of all values of $x$ for which the function is defined. The range of a function is the set of all values of $y$ that the function can take.

The domain of the function $y=f(x)$ is the set of all real numbers. This is because the function is defined for all real values of $x$.

The range of the function $y=f(x)$ is the set of all real numbers greater than or equal to 0. This is because the function can never take on negative values.

Increasing, Decreasing, and Constant Intervals

An interval on which a function is increasing is an interval on which the function values increase as the $x$-values increase. An interval on which a function is decreasing is an interval on which the function values decrease as the $x$-values increase. An interval on which a function is constant is an interval on which the function values do not change as the $x$-values increase.

The function $y=f(x)$ is increasing on the interval $(-\infty, 0)$ and decreasing on the interval $(0, \infty)$. The function is constant on the interval $[0, \infty)$.

X-Intercepts and Y-Intercepts

The x-intercept of a function is the point where the function crosses the $x$-axis. The y-intercept of a function is the point where the function crosses the $y$-axis.

The function $y=f(x)$ has one x-intercept at $x=0$ and one y-intercept at $y=0$.

Symmetry

A function is symmetric with respect to the y-axis if its graph is the same when reflected about the y-axis. A function is symmetric with respect to the origin if its graph is the same when reflected about the origin.

The function $y=f(x)$ is symmetric with respect to the y-axis. This is because the graph of the function is the same when reflected about the y-axis.

Examining the Graph Using Algebra

Writing an Equation for the Function

We can write an equation for the function $y=f(x)$ by using the following steps:

1. Find the slope of the function. The slope of the function is the change in $y$-values divided by the change in $x$-values.
2. Find the y-intercept of the function. The y-intercept of the function is the value of $y$ when $x=0$.

The slope of the function $y=f(x)$ is 1. The y-intercept of the function $y=f(x)$ is 0.

Therefore, the equation for the function $y=f(x)$ is $y=x$.

Finding the Derivative of the Function

The derivative of a function is a function that gives the rate of change of the function with respect to its independent variable.

The derivative of the function $y=f(x)$ is $f'(x)=1$.

Finding the Critical Points of the Function

A critical point of a function is a point on the graph of the function where the derivative is zero or .

The function $y=f(x)$ has one critical point at $x=0$.

Finding the Inflection Points of the Function

An inflection point of a function is a point on the graph of the function where the second derivative changes sign.

The function $y=f(x)$ does not have any inflection points.

Sketching the Graph of the Function

We can sketch the graph of the function $y=f(x)$ by using the following steps:

1. Plot the points $(-1, 1)$, $(0, 0)$, and $(1, 1)$.
2. Connect the points with a smooth curve.

The resulting graph is shown below.

[Image of the graph of the function $

Applying the Graph to Real-World Problems

The graph below shows the relationship between the height of a plant and the number of days since it was planted.

Plant growth curve

We can use this graph to solve a variety of problems involving rates of change. For example, we can use it to find the average rate of growth of the plant over a given period of time. To do this, we would simply divide the change in height by the change in time.

We can also use the graph to model a real-world phenomenon. For example, we could use it to model the growth of a population of bacteria. To do this, we would need to make some assumptions about the rate of growth of the bacteria. Once we have made these assumptions, we can use the graph to predict the size of the population at any given time.

Finally, we can use the graph to make predictions about the future. For example, we could use it to predict the height of a plant at a certain point in time. To do this, we would need to know the rate of growth of the plant and the initial height of the plant. Once we have this information, we can use the graph to extrapolate the plant’s growth and predict its height at a future date.

Evaluating the Graph

When evaluating a graph, it is important to consider a variety of factors, including:

  • The accuracy of the data
  • The clarity of the graph
  • The usefulness of the graph

The accuracy of the data is important because it determines how reliable the s drawn from the graph are. If the data is inaccurate, then the s drawn from the graph will also be inaccurate.

The clarity of the graph is also important because it determines how easy it is to understand the information that is being presented. If the graph is not clear, then it will be difficult for people to understand the information that is being presented and they may draw incorrect s.

Finally, the usefulness of the graph is important because it determines how valuable the information that is being presented is. If the graph is not useful, then people will not be able to use the information to make informed decisions.

When evaluating a graph, it is important to consider all of these factors in order to make a fair assessment of its quality.

In this article, we have discussed the different ways to apply a graph to real-world problems. We have also discussed the factors to consider when evaluating a graph. By understanding these concepts, you will be able to use graphs to make informed decisions and solve problems in a variety of contexts.

Which Function Is Graphed On The Coordinate Plane Below?

Q: What is the graph of the function $f(x) = x^2$?

A: The graph of the function $f(x) = x^2$ is a parabola that opens up and has its vertex at the origin. The graph is symmetric about the $y$-axis.

Q: What is the graph of the function $f(x) = \frac{1}{x}$?

A: The graph of the function $f(x) = \frac{1}{x}$ is a hyperbola that has its asymptotes at $x = 0$ and $y = 0$. The graph is symmetric about the origin.

Q: What is the graph of the function $f(x) = \sin(x)$?

A: The graph of the function $f(x) = \sin(x)$ is a sine wave that has its maximum value at $x = \frac{\pi}{2}$ and its minimum value at $x = -\frac{\pi}{2}$. The graph is symmetric about the $y$-axis.

Q: What is the graph of the function $f(x) = e^x$?

A: The graph of the function $f(x) = e^x$ is an exponential function that increases without bound as $x$ increases. The graph is symmetric about the $y$-axis.

we have seen that the graph of a function can be used to identify its properties. We can use the graph to find the domain and range of the function, the x-intercepts and y-intercepts, and the intervals where the function is increasing, decreasing, or constant. We can also use the graph to determine the relative minimum and maximum values of the function. By understanding the properties of a function’s graph, we can gain valuable insights into the behavior of the function.

Author Profile

Dale Richard
Dale Richard
Dale, in his mid-thirties, embodies the spirit of adventure and the love for the great outdoors. With a background in environmental science and a heart that beats for exploring the unexplored, Dale has hiked through the lush trails of the Appalachian Mountains, camped under the starlit skies of the Mojave Desert, and kayaked through the serene waters of the Great Lakes.

His adventures are not just about conquering new terrains but also about embracing the ethos of sustainable and responsible travel. Dale’s experiences, from navigating through dense forests to scaling remote peaks, bring a rich tapestry of stories, insights, and practical tips to our blog.