DSAT extra practice Ch2 Lv3

A certain opera house has 30 rows of seats. The first row has 12 seats, and the number of seats in each subsequent row is always 4 more than the row before it. If [math]f(n)[/math] represents the number of seats in the [math]n^{\text{th}}[/math] row, which of the following is incorrect?

The table shows some values of [math]x[/math] and their corresponding values of the exponential function [math]f(x)=a\cdot b^x[/math] where [math]a[/math] and [math]b[/math] are constants. What is the value of [math]c[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. If [math]g(x)=f(x+2)[/math], which of the following tables best represents [math]g(x)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. Which of the following functions could be [math]f(x)[/math]?

Let [math]f(x)[/math] be a function satisfying [math]f(x+3)=2f(x)[/math]. If [math]f(1)=2[/math], what is the value of [math]f(4)[/math]?

$$f(x)=k-\sqrt{x+4}$$If the [math]x[/math]-intercept of [math]f(x)[/math] is 0, what is the value of [math]k[/math]?

The figure above shows the graph of [math]f(x)=a\cdot b^x+c[/math] where [math]a, b[/math], and [math]c[/math] are constants. Which of the following statements is true?

The figure above shows the graph of [math]f(x)[/math]. How many solutions does the equation [math]f(x)=2[/math] have?

$$f(x)=\frac{2(x+2)}{(x-1)(x+2)}$$What is the domain of [math]f(x)[/math]?

$$f(x)=\sqrt{x^2+1}$$What os the range of [math]f(x)[/math]?

$$f(x)=2^{4-3x}-1$$Which of the following functions is equivalent to [math]f(x-2)[/math]?

$$f(x)=ax+b$$Which of the following is [math]g(f(x))[/math]?

$$f(x)=x(x+1)^{2023}$$$$g(x)=2024$$What is the value of [math]g(f(10))[/math]?

The table above shows some values of functions [math]f(x)[/math] and [math]g(x)[/math]. If [math]f(g(m))=3[/math], what is the value of [math]m[/math]?

$$\ell_1: y=mx+1$$$$\ell_2=nx-1$$If [math]\ell_1[/math] and [math]\ell_2[/math] intersect at the first quardrant, which of the following is true?

Let [math]f(x)=mx+12[/math] be a linear function. If [math]m\leq-4[/math], which of the following cannot be the [math]x[/math]-intercept of [math]f(x)[/math]?

$$\ell: y=m(x+2)-3$$The equation of line [math]\ell[/math] is shown above, which of the following points is on [math]\ell[/math]?

The graph of line [math]\ell[/math] is shown above, which of the following equations could be [math]\ell[/math]?

Two lines [math]\ell_1[/math] and [math]\ell_2[/math] are perpendicular and having the same [math]x[/math]-intercept. If the equation [math]\ell_1[/math] is [math]y=2x+6[/math], what is the equation of [math]\ell_2[/math]?

Let [math]A(1,7)[/math] and [math]B(5,-3)[/math] be two points on the [math]xy[/math]-plane. If line [math]\ell[/math] is perpendicular to [math]\overline{AB}[/math] and it passes through the midpoint of [math]A[/math] and [math]B[/math], what is the equation of [math]\ell[/math]?

Two lines [math]\ell_1[/math] and [math]\ell_2[/math] are perpendicular and their [math]y[/math]-intercepts are both [math]b[/math]. If the [math]x[/math]-intercept of [math]\ell_1[/math] is [math]2b[/math], what is the [math]x[/math]-intercept of [math]\ell_2[/math]?

There are 333 soldiers in a camp. Their general prepared 27 trucks to transport them to the front line. A small truck can carry 9 people and a big truck can carry 15 people. If all the trucks were filled to capacity, how many soldiers would ride in the small trucks?

$$2x+3+6=5x-y+4=-x-y+16$$If [math](x,y)=(a,b)[/math] is a solution to the equations system above, what is the value of [math]a+b[/math]?