Solution Bank Exponential & Logarithmic Functions Target A
Answers to the Practice Problems are below in random order.
Dom: \((-\infty,\infty)\), Rng: \((0,\infty)\), as \(x\rightarrow\infty, f(x)\rightarrow0\),as \(x\rightarrow-\infty, f(x)\rightarrow\infty\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 1)\) HA: \(y = 1\)
Dom: \((-\infty,\infty)\), Rng: \((25,\infty)\) HA: \(y = 25\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, -3)\), as \(x\rightarrow\infty, f(x)\rightarrow-3\), as \(x\rightarrow-\infty, f(x)\rightarrow-\infty\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 0)\), as \(x\rightarrow\infty, f(x)\rightarrow-\infty\), as \(x\rightarrow-\infty, f(x)\rightarrow0\)
Dom: \((-\infty,\infty)\), Rng: \((-5,-\infty)\) HA: \(y = -5\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 2)\), as \(x\rightarrow\infty, f(x)\rightarrow-\infty\), as \(x\rightarrow-\infty, f(x)\rightarrow2\)
Dom: \((-\infty,\infty)\), Rng: \((\infty,-2)\) HA: \(y = -2\)
Dom: \((-\infty,\infty)\), Rng: \((0, \infty)\), as \(x\rightarrow\infty, f(x)\rightarrow0\), as \(x\rightarrow-\infty, f(x)\rightarrow\infty\)
vertical stretch of \(3\)
vertical compression of \(\frac{1}{3}\), left \(4\)
vertical stretch of \(11\), left \(3\), flip over \(x\)-axis, up \(1\)
Shift right \(2\), Flip over \(x\) axis
\(\frac{1}{3}\)
\(4.5\)
\(\Large\frac{4}{9}\)
\(2x^2y + 2xy^2\)
\(15 - 6i\)
\(-1 + 12i\)
Answers to the Practice Problems are below in random order.
Dom: \((-\infty,\infty)\), Rng: \((0,\infty)\), as \(x\rightarrow\infty, f(x)\rightarrow0\),as \(x\rightarrow-\infty, f(x)\rightarrow\infty\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 1)\) HA: \(y = 1\)
Dom: \((-\infty,\infty)\), Rng: \((25,\infty)\) HA: \(y = 25\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, -3)\), as \(x\rightarrow\infty, f(x)\rightarrow-3\), as \(x\rightarrow-\infty, f(x)\rightarrow-\infty\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 0)\), as \(x\rightarrow\infty, f(x)\rightarrow-\infty\), as \(x\rightarrow-\infty, f(x)\rightarrow0\)
Dom: \((-\infty,\infty)\), Rng: \((-5,-\infty)\) HA: \(y = -5\)
Dom: \((-\infty,\infty)\), Rng: \((-\infty, 2)\), as \(x\rightarrow\infty, f(x)\rightarrow-\infty\), as \(x\rightarrow-\infty, f(x)\rightarrow2\)
Dom: \((-\infty,\infty)\), Rng: \((\infty,-2)\) HA: \(y = -2\)
Dom: \((-\infty,\infty)\), Rng: \((0, \infty)\), as \(x\rightarrow\infty, f(x)\rightarrow0\), as \(x\rightarrow-\infty, f(x)\rightarrow\infty\)
vertical stretch of \(3\)
vertical compression of \(\frac{1}{3}\), left \(4\)
vertical stretch of \(11\), left \(3\), flip over \(x\)-axis, up \(1\)
Shift right \(2\), Flip over \(x\) axis
\(\frac{1}{3}\)
\(4.5\)
\(\Large\frac{4}{9}\)
\(2x^2y + 2xy^2\)
\(15 - 6i\)
\(-1 + 12i\)