[Customized] DSAT final review 1 (Natalie W)

Let [math]f(x)=a|x-h|+k[/math] be a function with range [math](-\infty,3][/math] where [math]a, h[/math], and [math]k[/math] are constants. If [math]x=-2[/math] is the axis of symmetry of [math]f(x)[/math] and [math]f(0)=-1[/math], find, [math]a, h[/math], and [math]k[/math].

If [math]a\pm\sqrt{b}[/math] are the solutions to the equation [math](9-x)^2=2[/math], what is the value of [math]a+b[/math]?

(Calculator) Jean rows a boat 6 km downstream, and then turns around and rows the same distance home. The effect of the current on Jean’s boat is 3 km/hr. She spent 4.5 hours in total rowing. What is the speed, in km/hr, of the boat in still water? Round to the nearest hundredth.

$$\sqrt[n]{16}=2^n$$What is the solution to the equation above?

In the figure, [math]ABCD[/math] is a trapezoid and [math]ABED[/math] is a parallelogram. If [math]m\angle B=50^\circ[/math] and [math]m\angle C=70^\circ[/math], what is [math]m\angle CDE[/math]?

Let [math]C[/math] be a circle with center [math](1,-3)[/math]. If [math]P(1,3)[/math] is on [math]C[/math], what is the equation of [math]C[/math]?

The line graph above shows the number of 3 major crimes in New York from 2019 to 2023. Which of the following statements is false?

According to a 1920 regulation by the French government, the standard weight for a baguette should be approximately 250 grams. The owner of a traditional French bakery wants to verify if the baguettes in her bakery meets this standard. She randomly selects 120 baguettes and measures an average weight of 247 grams with a margin of error of 7 grams. Which of the following statements is correct?

If [math]f(x)=px+q[/math] and [math]f(f(f(x)))=8x+21[/math], determine [math]p[/math] and [math]q[/math] where [math]p,q\in\mathbb{R}[/math].

Let [math]f(x)=x^4-4x^2+8x-6[/math] and [math]g(x)=(2x-1)^2[/math]. Find the leading coefficients of following functions:

(a) [math]f(x)\cdot g(x)[/math]

(b) [math]f(g(x))[/math]

(c) [math]3f(x)+2g(x)[/math]

If a quadratic function [math]f(x)[/math] passes through [math](2,0)[/math] and the origin, which of the following equations could not be [math]f(x)[/math]?

A bottle of plum drink is 500 ml and contains 30% plum juice. If Mia poured half a bottle of plum drink and [math]x[/math] ml of plum juice into his mug, the concentration of plum juice in his drink becomes 50%. Which of the following equations best represent this situation?

$$\sqrt[3]{-8x^4y^7}$$If the expression above can be written as [math]ax^by^c\sqrt[3]{xy}[/math] where [math]a, b[/math], and [math]c[/math] are integers, what is the value of [math]a+b+c[/math]?

$$f(x)=3+\frac{5}{x-4}$$Which of the following equations is a horizontal asymptote of [math]f(x)[/math]?