This question asks us to evaluate an absolute value function at a specific point. To find f(1) where f(x) = |2x-5|, we substitute x = 1: f(1) = |2(1)-5| = |2-5| = |-3| = 3. The absolute value operation takes the distance from zero, so |-3| = 3. A common error is to forget to apply the absolute value after evaluating the expression inside, which would give -3 instead of 3. Always complete all operations inside the absolute value bars first, then take the absolute value of the result.

The question asks for $f(3)$ where $f(x)=2^{x+1}$. This is exponential, nonlinear with base 2. Substitute: $2^{3+1}=2^4=16$. The exponent is $x+1$, not $x$. A common error is forgetting +1, getting 8 like B. Another is miscalculating $2^3=8$. Apply the exponent correctly to avoid confusing with base changes.

The question requires the equation for a positive function through (0,2) with y=0 asymptote and through (-1,4). This is an exponential decay function, nonlinear approaching zero asymptotically. Points give: at x=0, a=2; at x=-1, 2*(1/b)=4, b=1/2, so $y=2*(1/2)^x$. Matches points and asymptote. Choice A fits; reciprocal lacks exponential shape. Common error: Choosing growth for increasing at negative x. Strategy: Use points from both sides of y-intercept to find base in exponentials.

The question asks for the car's value after 2 years, starting at $18,000 depreciating 15% yearly. This is exponential decay, nonlinear with factor 0.85. Calculate 18000 * 0.85^2 = 18000 * 0.7225 = 13005. Round to nearest dollar. A common error is subtracting like getting 12600 in C. Another is wrong calculation like A. Use decay formula and verify multiplication to avoid linear mistakes.

The question asks for r(6) where $r(x) = \frac{2x - 1}{x - 4}$. This is a rational function, nonlinear and evaluated by substitution. Plug in x=6: $\frac{12 - 1}{6 - 4} = \frac{11}{2}$. Simplify the fraction after substituting. A common error is mis-substituting like getting $\frac{1}{11}$. Another is confusing numerator and denominator. For rationals, substitute carefully and simplify to avoid arithmetic errors.

The question requires finding $g(-5)$ for $g(x) = \dfrac{x}{x+5}$, noting it's nonlinear. This is a rational function, nonlinear with a possible asymptote. At $x=-5$, denominator $-5 + 5 = 0$, so undefined. Division by zero makes it undefined, not a real number. Matches choice C. A common error is attempting to compute it as $-5/0$ = some value. Strategy: Check denominator for zero before evaluating rational functions to identify undefined points.

The question asks for the domain description of f(x) = 3x/(x - 1). This is a rational function, nonlinear undefined where denominator is zero. Set x - 1 ≠ 0, so x ≠ 1, domain all reals except 1. Matches choice C. Other restrictions like x ≥ 1 are for square roots. A key error is assuming no restrictions like polynomials. Strategy: Identify denominator zeros to define domains for rational functions, excluding those points.

This question asks for the equation defining f(x) given f(0)=7 and multiplication by 4 for each unit increase in x. The function is exponential growth, as the output multiplies by a constant factor, unlike linear addition or polynomial powers. Starting with f(0)=7, then f(1)=74, $f(2)=74^2$, so generally $f(x)=7*4^x$. Choice B has the base and initial swapped. A common error is selecting a linear model like 7+4x, which adds instead of multiplies. For recursive descriptions, convert to explicit exponential form by identifying the initial value and growth factor.

This question asks for an exponential decay model for a depreciating car. When something depreciates by 12% each year, it retains 88% (or 0.88) of its value. The exponential decay formula is V(t) = $V₀(1-r)^t$, where V₀ is the initial value and r is the decay rate. With V₀ = 18000 and r = 0.12, we get V(t) = $18000(1-0.12)^t$ = $18000(0.88)^t$. A common mistake is to use 1.12 instead of 0.88, which would represent growth rather than decay. Remember that depreciation means the value decreases, so the base of the exponential must be less than 1.

This question asks us to find the number of bacteria cells after 9 hours using the given exponential growth model. The function N(t) = 500·2^(t/3) is an exponential function where the bacteria population doubles every 3 hours. To find the number of cells after 9 hours, we substitute t = 9 into the formula: N(9) = 500·2^(9/3) = $500·2^3$ = 500·8 = 4000. A common error is to use $2^9$ instead of 2^(9/3), which would give an incorrect answer of 256,000 cells. When dealing with exponential growth problems, always check that the exponent correctly reflects the given time period and growth rate.