Question

The graph of f(x) = x + 1 is shown in the figure. Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 3| < 0.4.

Answer 1

SO what you need to do is:
Start with |f(x) - 3| < 0.4
and plug in f(x) = x+1
to get |f(x) – 3| < 0.4
|x+1 – 3| < 0.4
|x - 2| < 0.4
   -0.4 < x - 2 < 0.4
  -0.4+2 < x < 0.4+2
  1.6 < x < 2.4
So delta would be 2.3
Hope this is what you were looking for

Answer 2

The largest δ such that if 0 < |x – 2| < δ is 0.4

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {m = \frac{y_2 - y_1}{x_2 - x_1}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$y - y_1 = m ( x - x_1 )$

Let us tackle the problem.

Given:

$f(x) = x + 1$

If $|f(x) - 3| < 0.4$ , then :

$|f(x) - 3| < 0.4$

$|x + 1 - 3| < 0.4$

$|x -2| < 0.4$

Since the absolute value of a function is always positive, then:

$0 < |x -2| < 0.4$

From the relationship above, then the largest δ such that :

$0 < |x - 2| < \delta$

→ δ = 0.4

Learn more

• Infinite Number of Solutions : https://brainly.com/question/5450548
• System of Equations : https://brainly.com/question/1995493
• System of Linear equations : https://brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point