Question

let f be the function defined on [-1,3] such that f(x)=2x-1.plot the graph of f and determine its domain and range.

Answer 1

Given info : Let f be the function defined on [-1, 3] such that f(x) = 2x - 1

To find : Plot the graph of function f and determine its domain and range.

solution : Domain is the interval in which function is defined and range is the value of dependent variable after substituting domain.

for example, a function, y = f(x) is defined on interval [a, b] then [a, b] is domain and range is values of y on [a, b]

here domain belongs to [-1, 3]

i.e., -1 ≤ x ≤ 3

⇒-1 × 2 ≤ 2x ≤ 2 × 3

⇒-2 ≤ 2x ≤ 6

⇒-2 - 1 ≤ 2x - 1 ≤ 6 - 1

⇒-3 ≤ f(x) ≤ 5

Therefore the range of function belongs to [-3, 5]

see plotted graph attached in answer.