Question

Draw y = |x-5|+10. * 1.Is this function continuous at each point on the real line? 2. Is this function differentiable at each point on the real line?

Answer 1

(1) The function is continuous at each point on the real line

(2) The function is not differentiable at each point on the real line

Step-by-step explanation:

In order to draw the graph of the function we take following steps

• We know the graph of |x|, therefore to draw the graph of |x-5| we shift the graph by 5 units to the right
• Then we shift the graph to 10 units above the y-axis and thus we get the graph of |x-5|+10

As we can see that the function $|x-5|+10$ is defined for all $x\in R$

Therefore, the function is continuous on the real line

Since there is a sharp turn at x = 5

Therefore, the function is not differentiable at x = 5

Thus, the function is not differentiable at each point on the real line

Hope this answer is helpful.

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