How To Find The Range Of An Exponential Function

Detect Range of Exponential Functions

Observe the range of real valued exponential functions using unlike techniques. Matched problems are too included with their answers at the bottom of the page.

Examples with Solutions Example 1 Detect the Range of part f divers by Solution to Case 1 Matched Problem one: Find the range of function f defined past Example 2 Find the Range of function f divers past Solution to Example two Matched Problem 2: Find the range of part f defined past Example 3 Find the Range of function f defined by Solution to Example three Write the given office as an equation Solve the above for x to obtain x2 = ln(y - ane) 10 = + or - √[ ln(y - 1) ] The to a higher place solutions are real if ln(y - 1) ≥ 0 y - 1 ≥ ane y ≥ two Hence the range of the given function is given by y ≥ 2 or in interval form [ 2 , + ∞ ) See graph of f beneath and examine the range graphically. Matched Problem three: Notice the range of function f defined by Example iv Find the Range of function f defined by Solution to Case 4 We first write the given part as an equation as follows Solve the in a higher place for x y - 3 = -2 eastward-10ii due east-x2 = (y - 3) / (-2) -x2 = ln [ (y - 3) / (-2) ] x = + or - √( - ln [ (y - 3) / (-2) ]) x is real if the argument of ln is positive and the radicand is positive or zero. Hence the following inequalities (y - 3) / (-two) > 0 and - ln [ (y - three) / (-2) ] ≥ 0 the solution set of (y - 3) / (-2) > 0 is y < three the solution gear up of - ln [ (y - 3) / (-2) ] ≥ 0 is given past (y - 3) / (-2) ≤ 1 which gives y ≥ 1 the range of f is given by 1 ≤ y < 3 or in interval form [ ane , 3 ) Encounter graph of f below and examine the range graphically. Matched Trouble 4: Find the range of function f defined by Answers to Matched Issues 1. (0 , +∞) 2. (-∞ , -ii) 3. (-∞ , -6] 4. (-7 , -3] More References and Links Find the domain of a office mathematics tutorials and problems.

Source: https://www.analyzemath.com/DomainRange/find_range_exponential.html

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