A graph of a function is a plot of the values of a function over some range of its independent variable(s). Graphs are useful for visualizing and understanding relationships between variables.

A function is simply a line that shows a relationship between two variables. For example, the equation y5x+3 tells us that when x increases by 3, the value of y also increases by 5.

Functions are extremely useful in everyday life. They show relationships between things such as age and height, or sales and profits. Understanding functions is essential for understanding calculus and statistics.

There are several types of graphs that can represent a function. The most common type is called a Cartesian coordinate graph.

What is the graph of $f(x)2x^3+1$?

**Step-by-step explanation:**

To check whether the graph represents a function or not, we perform vertical line test.

**Vertical Line test:**

You’ve probably heard of the vertical line test before, but did you know that you can apply it to functions too?

**The vertical line test helps determine whether a function is increasing or decreasing by plotting two lines on top of each other.**

To perform the vertical line test, plot the y-axis on top of the x-axis and then draw a horizontal line through the points where the values differ. If the resulting graph looks like the picture above, the function is increasing. If the graph looks like the picture below, the function is decreasing.

If any vertical line cuts and intersects a graph at exactly one point then the graph is representing a function else you can say its not representing any function.

For the question to choose Which graph represents a function from the below graph options .

Check all the graphs and find vertical lines which intersects and only one place

and that is in the graph D .

**Hence, graph D represents a function.**

**Horizontal Line test:** This is to calculate the inverse of the function.

The Horizontal Line Test (HLT) is a method for determining whether or not a given function has a horizontal tangent at a certain point.

If the slope of the line through two points is parallel to the axis, then the function has a horizontal tangential line at those points.

## Graph of a function types

### Horizontal line test

The horizontal line test is a simple way to determine if a function is increasing or decreasing. If the graph looks like a straight line, then the function is said to be constant. A horizontal line means that the value of the function stays the same over time.

### Vertical Line Test

If the graph looks like a vertical line, then the function increases or decreases exponentially. In this case, the graph would look like a straight line with a slope of 1.0.

### Linear Trendline

A linear trendline is a line that goes through the points on a graph. It’s useful when looking at data that doesn’t have any trends.

### Quadratic Curve

A quadratic curve is a curved line that follows the pattern y ax^2 + bx + c. The x-axis is called the independent variable, while the y-axis is known as the dependent variable.

### Exponential Growth

If for example the graph x axis represents time, and the y axis represents the value of each function at that point. And the functions start out slowly and then begin increasing much faster. This type of growth is called exponential growth because it grows by multiplying itself.

### How to determine which graph represents a function?

The vertical line test helps determine whether a function is increasing or decreasing by plotting two lines on top of each other. If vertical lines which intersects and only one place its a function.

### Define graph of a function?

The graph of a function is a visual representation of the relationship between two variables. In other words, it shows where the values of those variables lie on the same axis.

Graphs can be used to represent functions or data sets. They are usually plotted using coordinates, such as x and y axes.

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