f(x) = x^2 - 1 g(x) = -x^2 + 4
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Step 1
First, we need to graph the functions f(x) = x^2 - 1 and g(x) = -x^2 + 4. We already have the graphs of these functions, as described in the question. Show more…
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The function $f$ graphed below is defined by a polynomial expression of degree $4 .$ Use the graph to solve the exercises. a. To solve the equation $2 x+1=-x+4$ graphically, we graph the functions $f(x)=$ ____ and $g(x)=$ ___ on the same set of axes and determine the values of $x$ at which the graphs of $f$ and $g$ intersect. Graph $f$ and $g$ below, and use the graphs to solve the equation. The solution is $x=$ ____ . b. To solve the inequality $2 x+1<-x+4$ graphically, we graph the functions $f(x)=$ ___ $\operatorname{and} g(x)=$ ___ on the same set of axes and find the values of $x$ at which the graph of $g$ is ____ (higher/lower) than the graph of $f$. From the graphs in part (a) we see that the solution of the inequality is the interval ( ____, ____)
Functions
Getting Information from the Graph of a Function
Graph f and g below. Use the graphs to solve the equation.
Gregory H.
(a) To solve the equation $2 x+1=-x+4$ graphically, we graph the functions $f(x)=$ __________ and $g(x)=$ __________ on the same set of axes and determine the values of $x$ at which the graphs of $f$ and $g$ intersect. Graph $f$ and $g$ below, and use the graphs to solve the equation. The solution is $x=$ ______ . (b) To solve the inequality $2 x+1<-x+4$ graphically, we graph the functions $f(x)=$ __________ and $g(x)=$ ______________ on the same set of axes and find the values of $x$ at which the graph of $g$ is ____________ (higher/lower) than the graph of $f$. From the graphs in part (a) we see that the solution of the inequality is the interval ( _____, _____ ).
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