Math  /  Algebra

QuestionIdentify functions with a range of {yR<y<}\{y \in \mathbb{R} \mid-\infty<y<\infty\}:
1. f(x)=23x8f(x)=\frac{2}{3} x-8
2. f(x)=x2+7x9f(x)=x^{2}+7 x-9
3. f(x)=4x+11f(x)=-4 x+11
4. f(x)=(x+1)24f(x)=-(x+1)^{2}-4
5. f(x)=2x+3f(x)=2^{x+3}

Studdy Solution
Finally, consider the function f(x)=2x+3f(x)=2^{x+3}. This is an exponential function, and the range of an exponential function is 0<y<0<y<\infty. Therefore, the fifth function does not have the given range.
So, the functions that have a range of {yR<y<}\{y \in \mathbb{R} \mid-\infty<y<\infty\} aref(x)=23x8f(x)=4x+11\begin{array}{l} f(x)=\frac{2}{3} x-8 \\ f(x)=-4 x+11\end{array}

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