*label*Mathematics

### Question Description

Do not use your calculator for Parts 1 through 4.

Let *f* be the function defined as follows:

- If a = 2 and b = 3, is
*f*continuous at x = 1? Justify your answer. - Find a relationship between a and b for which
*f*is continuous at x = 1.

Hint: A relationship between a and b just means an equation in a and b. - Find a relationship between a and b so that
*f*is continuous at x = 2. - Use your equations from parts (ii) and (iii) to find the values of a and b so that
*f*is continuous at both x = 1 and also at x = 2? - Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into the document.

## Tutor Answer

I've finished the questions, just reviewing them

Hey, Here are the answers

1. if a = 2 and b = 3 at x = 1 the function:

• For the part 3 − x, f (x) = 3 − 1 = 2

• For the part ax2 + bx = 2x2 + 3x = 2 × 1 + 3 × 1 = 5. The two parts of the f...

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