Function Graphs: Solving Questions with Step-by-Step Guide

[tigerd12]

Hey all

Recently in a paper I was doing I came across a question which involved the graphing of a function. Now I am doing GCSE mathematics (the real exam) soon, having finished the syllabus; and have never come across anything like this before!

Here's the question

The graph y=f(x) is drawn

Find f(3)

Attempt: Do I go 3 along the X axis then go up see where it cuts the graph, draw a line there and find solutions?

Find f(x)=6

Attempt: Do I draw the line y=6 and see where this intersects with the graph? giving solutions

Find ff(1)?

Attempt: Do I.. do f(1), meaning go 1 across on the X axis, find the solution where it cuts the graph and go across to see the Y value, then after I obtain this value go along the X axis and find the point of intersection?

Thanks for any help, I really don't understand! I have never seen this type of question before

 

[EnumaElish]

f(3): your thinking is correct.

f(x)=6: correct, then you "look down" to the x axis.

ff(1): I guess that means f(f(1)). After you find y = f(1), go across the X axis to find y on the X axis, then find f(y).

 

[Architeuthis Dux]

I would advise the following step-by-step guide to solving these types of function graph questions:

1. Start by understanding the basic concept of a function graph. A function is a relationship between two variables, typically represented by the letters x and y. In a function, every input (x) has only one output (y). The graph of a function shows this relationship visually.

2. Identify the given function, in this case, y=f(x). This means that the output (y) is dependent on the input (x).

3. For the first question, finding f(3), you need to substitute x=3 into the function. This means that you will find the value of y when x=3. So, go to the point where x=3 on the x-axis and see where it intersects with the graph. Then, read the corresponding y-value on the y-axis. This is your answer for f(3).

4. For the second question, finding f(x)=6, you need to find the x-values for which y=6. This means that you will draw a horizontal line at y=6 and see where it intersects with the graph. The x-values at these points are your solutions for f(x)=6.

5. For the third question, finding ff(1), you need to evaluate the function twice. Start by finding f(1) using the same steps as in question 1. Then, take the value you obtained for y and use it as the input for the function again. This means you will find f(y) using the value you obtained for f(1). Follow the same steps as in question 1 to find the final answer.

Remember to always label your axes and clearly indicate your solutions on the graph. Practice with different functions to improve your understanding of function graphs. Good luck on your exam!