Prove that the function `f(x) = 5x-3`is continuous at `x = 0`, at `x =-3`and at `x = 5`.

Explanation

To prove that the function \( f(x) = 5x - 3 \) is continuous at \( x = 0 \), \( x = -3 \), and \( x = 5 \), we will use the definition of continuity. A function is continuous at a point \( c \) if the following three conditions are satisfied:

1. \( f(c) \) is defined.
2. The limit of \( f(x) \) as \( x \) approaches \( c \) exists.
3. The limit of \( f(x) \) as \( x \) approaches \( c \) is equal to \( f(c) \).

### Step 1: Check continuity at \( x = 0 \)

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