the graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about…
the graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about the domain and range of each function is correct? the range of the transformed function and the parent function are both all real numbers greater than or equal to 4. the domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. the range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. the domain of the transformed function and the parent function are both all real numbers.
Answer
Explanation:
Step1: Find the transformed - function
The parent function is (y = f(x)=\vert x\vert). A vertical stretch by a factor of (a = 0.3) and a vertical translation down by (k = 4) units gives the new function (y=0.3\vert x\vert-4).
Step2: Analyze the domain
The domain of the parent function (y = \vert x\vert) is all real numbers ((x\in(-\infty,\infty))) because we can input any real - number into the absolute - value function. For the transformed function (y = 0.3\vert x\vert-4), we can also input any real number for (x). So the domain of both the parent function and the transformed function is all real numbers.
Step3: Analyze the range
The range of the parent function (y=\vert x\vert) is (y\geq0) since the absolute - value of any real number is non - negative. For the transformed function (y = 0.3\vert x\vert-4), the minimum value occurs when (x = 0). When (x = 0), (y=-4). So the range of the transformed function is (y\geq - 4).
Answer:
D. The domain of the transformed function and the parent function are both all real numbers.