Question

Graph each function. Give the domain and range. ƒ(x) = 2x+2 - 4

Accepted Answer

Identify the base function and its transformations. The base function here is the exponential function $$f(x) = 2^x. $$The given function is $$f(x) = 2$$^{x+2}$$ - 4$$, which involves a horizontal shift and a vertical shift. Determine the horizontal shift by analyzing the exponent $$x + 2. $$Since it is $$x + 2$$, this represents a shift to the left by 2 units compared to the base function $$2^x. $$Determine the vertical shift by looking at the $$-4$$ outside the exponential. This means the entire graph of $$2^{x+2} is $$shifted downward by 4 units. Find the domain and range of the function. The domain of any exponential function $$2^x is $$all real numbers, so the domain of $$f(x) = 2$$^{x+2}$$ - 4 is $$also all real numbers. The range of the base function $$2^x is$$ $$(0, \, \infty)$$, so after shifting down by 4, the range becomes $$(-4, \, \infty). To $$graph the function, start by plotting key points of the base function $$2^x$$, shift them left by 2 units, then shift down by 4 units. Draw a smooth curve through these points, remembering the horizontal asymptote is now at $$y = -4.$$

Graph each function. Give the domain and range. ƒ(x) = 2^x+2 - 4

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Exponential Functions

Domain and Range of Functions

Transformations of Functions