Test
Rational, exponential and logarithmic inequalities
This test develops methods for rational, exponential and logarithmic inequalities. Students use the interval method, account for monotonicity of exponential or logarithmic functions and enforce all domain restrictions.
Time left: 00:00:00
Sample questions
- Solve (x − (___))/(x − (___)) > 0.
- Solve (x − (___))/(x − (___)) < 0.
- For ___ > 1, solve ___x > ______.
- For 0 < ___ < 1, solve ___x > ______.
- Solve the logarithmic equation containing a sum of two logarithms.
Rational, exponential and logarithmic inequalities
Solve a rational inequality with a sign chart based on zeros of its numerator and denominator. Denominator zeros are never included, even with ≤ or ≥.
Monotonicity and domains
For an exponential base a > 1, the direction of an exponent inequality is preserved; for 0 < a < 1, it reverses. Logarithmic inequalities follow the same increasing or decreasing behaviour, but every argument must first be positive. Give the final answer as the intersection of all permitted intervals.
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