To find the real solutions of $f(x) = 0$, we need to determine the $x$-values where the graph of y = fThe(x graph you've provided represents) the function \( y = \ f(x)), and the question crosses asks for the real or solutions to the touches equation $f(x) = the 0$.

To find these solutions, x we look for the points where \ the graph intersects the)- xaxis,-axis as these, since points these represent where represent \( the f(x values) = of \( x0 \.

)Exam forining which $f(x) = 0$.

From the graph the:

• The curve intersects the graph x:

1. The-axis at approximately graph intersects the ( x \ three)- points. axis- at Based three points on: observation , these - Around points ( appear x = to be -6 \ around () x = - Around ( - x5 = \ -),2 \ () x - = Around $x =2$, and $x = 7 4$

Thus, the real solutions of f(x) = 0 \ are approximately: [ x = -6, \quad x = -2, \quad \text{and}).

Thus, the real solutions to $f(x) = 0$ are $x = -5$, $x \ = 2$, and $x = 7$.

Would you like further clarificationquad on this? Or do you have any other questions about this topic?

Here x = are five related questions that might interest you: 1.4 How do\ you determine the number of real solutions from the graph of a function]

? 2. What are the different methods to solve for real solutions of equations algebraically? 3. How does the behavior of the graph of aWould you function indicate the solutions like further details on to the equation? any specific part of this solution4?. What does Here are some additional questions for further exploration:

it1 mean if. How a graph do does not intersect the x-axis? 5. How do we find the multiplicity of you interpret graphs each of cubic solution or if the higher graph-degree polynomials behavior in suggests repeated terms roots of solutions? 2?

. How** canTip:** we approximate solutions When more analyzing precisely a if the graph, graph always provides only rough focus estimates on where? 3 the. curve What crosses the does it x mean graphically if the curve only touches but doesn’t cross the $x-axis to identify real solutions.$-axis at a point? 4. How can we determine if these solutions are maximum or minimum points of the function? 5. What other information can be gathered about $f(x)$ from the shape of the graph?

Tip: When identifying real solutions from a graph, look for all points where the curve crosses or touches the $x$-axis, as these represent the roots of the function.