Test Review Exponential and Logarithmic Functions and Equations PDF

# Test Review: Exponential and Logarithmic Functions and Equations ## 1. How can you determine whether an equation is exponential growth or exponential decay? Give two examples of each. * if b>1 growth * if 0<b<1 decay ## 2. Write the equation of each exponential function given two points. * a)...

# Test Review: Exponential and Logarithmic Functions and Equations ## 1. How can you determine whether an equation is exponential growth or exponential decay? Give two examples of each. * if b>1 growth * if 0<b<1 decay ## 2. Write the equation of each exponential function given two points. * a) (0, 4) and (1, 20) * 4=ab⁰ * 20=ab¹ * b=5 * 20=4b * y= 4(5)^x * b) (-2, 16) and (2, 1) * 16=ab² * 1=ab⁴ * 1=a(2)⁴ * a=1/16 * 16=1/16b² * b=2 * y=(1/16)(2)^x ## 3-6. Evaluate each expression or state that the expression is invalid. Write an exponential equation to support each choice. * 3. log₅ 1 = 0 * 4. log₃ 3 = 1 * 5. log₂ 0 = NO Possible * 6. log₂(1/2) = -1 * (1/2) = 2⁻¹ ## 7. Expand * a. log (27x⁵y⁻¹z) = log27 + log x⁵ + log y⁻¹ + log z * =log27 + 5logx - logy + log z ## 8. Condense * a. log (x + 1) - log (x) + log (2) * = log((x+1)²/x) + log 2 * = log((x+1)² * 2 / x) * b. -ln(x) + 3ln(y) - 6ln(z) * = ln(x⁻¹) + ln(y³) - ln(z⁶) * = ln(y³/x * z⁶) * c. -log₃(x) - log₃(8) - 2log₃(y) * = -log₃(x*8*y²) * = -log₃(8xy²) ## 9. Find the inverse for each function: * a. g(x) = 3x + 4 * x = 3g + 4 * x - 4 = 3g - 4 * log₃(x - 4) = g * g⁻¹(x) = log₃(x - 4) * b. h(x) = 5log₃(x + 2) * x = 5log₃(y + 2) * x/5 = log₃(y + 2) * 3^(x/5) = y + 2 * h⁻¹(x) = 3^(x/5) - 2 ## 10. Graph * a) g(x) = log₅(x - 2) + 1. * Domain: (2,∞) * Range: (-∞,∞) * Asymptote: x = 2 * y-intercept: NONE * Increasing: (2,∞) * End Behavior: * as x→∞ f(x)→∞ * as x→2⁻ f(x)→-∞ * b) g(x) = -3x⁻¹ + 5 * Domain: (-∞,∞) * Range: (-∞, 5) * Asymptote: y = 5 * y-intercept: (0, 14/3) * Decreasing: (-∞,∞) * End Behavior: * as x→∞ f(x)→5 * as x→∞ f(x)→5