Question

1. # Which Statements Are True About The Graph Of The Function F(X) = 6X – 4 + X2?

Graphs are a great way of visualizing data, and they can be especially helpful when understanding mathematical functions. In this blog post, we’ll focus on the graph of the function f(x) = 6x – 4 + x2 and which statements about it are true. By breaking down each part of the graph, we’ll gain a better understanding of how graphs work and what information can be inferred from them. Read on to learn more about the graph of f(x) = 6x – 4 + x2 and which statements are true!

## The function is continuous for all values of x

The function is continuous for all values of x. The graph of the function is a straight line. The function is differentiable for all values of x. The function is monotonic for all values of x.

## The function is differentiable for all values of x

Differentiability is a concept in calculus that describes the rate of change of a function at a given point. A function is said to be differentiable at a point x if the derivative exists at that point. The derivative of a function f(x) at a point x is denoted by f'(x) and is defined as the limit:

f'(x) = lim h→0 (f(x+h)-f(x))/h

This means that the derivative of a function f(x) at a point x is equal to the limit of (f(x+h)-f(x))/h as h approaches zero. In other words, it is the slope of the tangent line to the graph of the function at the point x.

The following three conditions are equivalent and together are necessary and sufficient for a function to be differentiable at a point:
* The function is continuous at that point.
* The derivative exists at that point.
* The tangent line exists at that point.

## The function is increasing for all values of x

The function is increasing for all values of x. This can be seen by the fact that the function is always positive and the slope is always positive.

## The function has a local minimum at x = 2

As you can see from the graph, the function has a local minimum at x = 2. This means that, for values of x near 2, the function takes on smaller values than it does at other nearby points. In other words, the graph “hugs” the x-axis more tightly at this point than it does elsewhere.

## The function has a global minimum at x = -2

The graph of the function F(x) = x – + x has a global minimum at x = -2. The y-value of the global minimum is -4. To find the global minimum, we set the derivative of the function equal to 0 and solve for x. The derivative of the function is F'(x) = 1 – . Setting this equal to 0 and solving for x gives us x = -2. Substituting this value into the original function gives us a y-value of -4, which is the global minimum.

## The function has an inverse for all values of x except where the function is not one-to-one

The graph of the function F(x) = x – + x has an inverse for all values of x except where the function is not one-to-one. In other words, the inverse of the function F(x) = x – + x is only defined for those values of x for which the function F(x) is one-to-one.

## The graph of the inverse function

The graph of the function f(x) = x – + x is shown below.

As you can see, the graph of the function is a straight line. The inverse function is also a straight line. However, the inverse function is not the same as the function itself. The inverse function is defined as follows:

If f(x) = y, then g(y) = x .

In other words, the inverse function takes the output of the original function and produces the input. So, if we were to graph the inverse function, it would look like this:

As you can see, the graph of the inverse function is a mirror image of the original function’s graph. It is important to note that not all functions have an inverse function. For example, a constant function (such as f(x) = 2) does not have an inverse because its output is always the same, no matter what input you give it.

2. Have you ever been stumped by a math problem?

If so, you’re not alone! Graphs can be tricky to interpret, but with a little practice, you can get the hang of it. Let’s take a look at the graph of the function f(x) = 6x – 4 + x2.

So, which statements are true about the graph of the function? Check all that apply.

✅ The graph of the function is a parabola with a single vertex.

The graph of the function is a parabola, meaning it has a curved line that opens either up or down. The single vertex is the point at which the parabola changes direction.

✅ The graph of the function has a maximum value.

The maximum value of a function is the largest value that can be obtained when the function is evaluated. In this case, the maximum value is obtained when x = 1.

✅ The graph of the function has a minimum value.

Similarly, the minimum value of a function is the smallest value that can be obtained when the function is evaluated. In this case, the minimum value is obtained when x = -2.

✅ The graph of the function is symmetrical about the y-axis.

Symmetry means that a figure looks the same on both sides of a line or an axis. In this case, the graph is symmetrical about the y-axis, meaning that if you draw a vertical line through the center of the graph, the two halves of the graph will look the same.

There you have it! With a little practice and practice, you can now easily interpret graphs like this one.