2.1 Basic functions (graphs and values)

If [math]f(x)=-7x+120[/math], what is the minimum integer [math]n[/math] such that [math]f(n)[/math] is negative?

The figures below show the graphs of [math]f(x)[/math] and [math]g(x)[/math]. Answer the following questions. Note: If your answer is undefined, write “undef”.

(a) [math]f(-5)+g(1)[/math]

(b) [math]f(g(-1)+1)[/math]

(c) How many integer solutions to the inequality [math]f(x)\geq2[/math]?

(d) How many constants [math]c[/math] satisfy [math]g(c)=1[/math]?

(e) Let [math]p(x)=f(x)+g(x)[/math]. Find [math]p(2)[/math].

(f) Let [math]q(x)=f(x)g(x)[/math]. Find [math]q(5)[/math].

(g) Let [math]r(x)=g(-f(3x-1))[/math]. Find [math]r(2)[/math].

(h) How many intersection of [math]f(x)[/math] and [math]g(x)[/math] are there?

The figure below shows the graph of function [math]f(x)[/math]. The domain of [math]f(x)[/math] is [math][-6,6][/math] and [math]f(-1.5)=2[/math].

(a) Find all possible values of [math]m[/math] such that [math]f(m)=3[/math]. Write your answers in ascending order.

(b) Find the conditions of [math]k[/math] such that the equation [math]f(x)=k[/math] has 4 solutions.

(c) Evaluate [math]f(f(5))[/math].

(d) If [math]g(x)[/math] is a linear function and [math]g(x)[/math] and [math]f(x)[/math] have common [math]x[/math]-intercept and [math]y[/math]-intercept, what is the equation of [math]g(x)[/math]?

(e) Find the domain of [math]f(g(x))[/math].

(f) Solve the inequality [math]f(x)<g(x)[/math].

Let [math]f(x)=-2|x|+3[/math] and [math]g(x)=\sqrt{x}-5[/math].

(a) Evaluate [math]f(g(4))[/math].

(b) Find the [math]x[/math]-intercept(s) of [math]f(g(x))[/math]. If you have two or more answers, write the smallest one.

The figure below shows the graph of [math]f(x)[/math].

(a) How many possible integers [math]n[/math] such that [math]f(n)[/math] is negative?

(b) The summation of the [math]x[/math]-intercepts and the [math]y[/math]-intercept of [math]f(x)[/math] is \underline{ (positive/negative/zero) }

(c) Let [math]m[/math] be a positive number. If [math]g(x)=mx-1[/math] and [math]f(x)[/math] have three intersections, then the range of [math]m[/math] is [math]a<m<b[/math] where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]ab[/math]?

The figure below shows the graph of [math]f[/math], which of the following statements is/are true?

The function [math]h(t)=20t-5t^2[/math] gives the height of an object [math]t[/math] seconds after it has been thrown into the air. Which statement is true?

(Calculator) [math]f(x)=\sqrt{2x-1}+k[/math], [math]f(3)=15.28[/math], then the value of [math]k[/math]?

(Calculator) [math]f(x)=x^5-2x+7[/math], [math]-1\leq x\leq1[/math], what is the minimum value of [math]f(x)[/math]?

If [math]f(x)=3xg(x)[/math] and [math]f(3)=6[/math], then [math]g(3)[/math]

If [math]f(x)=\sqrt{x^3+8}[/math], how much does [math]f(x)[/math] increase as [math]x[/math] increases from 4 to 5?

The figure below shows the graphs of functions [math]f[/math] and [math]g[/math]. Which of the following is closest to a value of [math]x[/math] such that [math]f(x)-g(x)=0[/math]?

(Calculator) If [math]f(x)=-x^3+4x^2-2x+2[/math], the maximum value of [math]f(x)[/math] on the interval [math][-2,4][/math] occurs when [math]x=[/math]

(Calculator) What is the range of the function [math]f[/math] defined by [math]f(x)=3x^{-2}-2[/math]?

A portion of the graph of [math]y=f(x)[/math] is shown below. Which of the following is the graph of [math]y=-|f(x)|[/math]?

If the function [math]f[/math] is symmetric with respect to the line [math]x=3[/math] and if [math]f(-1)=-1[/math], what is the value of [math]f(7)[/math]?

(Calculator) A function [math]f[/math] has the property that [math]f(\frac{x}{2})=\sqrt{\frac{1+f(x)}{2}}[/math] for [math]0\leq x\leq1[/math]. If [math]f(a)=0[/math], where [math]0\leq a\leq1[/math], what is the value of [math]f(\frac{a}{4})[/math]?