Big Ideas Math Algebra 1 Student Journal 1st Edition Chapter 3 Graphing Linear Functions
Page 6 Essential Question 9 Answer
To explain how do we use function notation to represent a function.
Using the method of function.
The notation y=f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value or independent variable.
The letter y, or f(x), represents the output value, or dependent variable.
The function notation represents a function that is y=f(x).
Read and Learn More Big Ideas Math Algebra 1 Student Journal 1st Edition Solutions
Page 69 Exercise 1 Answer
Given: Function is f(x)=2x−3 To graph the function in the graph
The given expression is f(x) = 2x-3 Now to graph the given expression
The graph that represents the expression f(x)=2x−3
The given expression is g(x)=x+2 Now to graph the given expression
The solution for the given expression g(x)=x+2 is
So the question has no solution.
The given expression is h(x)=x2−1 Now to graph the equation
The solution for the given expression h(x)=x2−1 is
The given expression is j(x)=2x2−3 Now to graph the given expression
The solution for the given expression j(x)=2x2−3 is
Page 70 Exercise 2 Answer
Given: Function is f(x)=x+3
To graph the given function.
Using the method of function.
The given function is f(x)=x+3
Now substitute x=−1, we get,
f(−1)=−1+3
f(−1)=2
Then the point is(−1,2)
Now to draw a graph with the given function and mark the point(−1,2)
The solution for the given function f(x)=x+3 is
Given: Function is f(x)=x+3
To graph the given function.
Using the method of function.
The given function is f(x)=x+3
Now substitute x=0,
f(0)=0+3
f(0)=3
Then the point is(0,3)
To graph the function with the point (0,3)
The solution for the given function f(x)=x+3 is
Given: Function is
f(x)=x+3
To graph the given function.
Using the method of function.
The given function is f(x)=x+3
Now substitute x=1
f(1)=1+3
f(1)=4
Then the point is(1,4)
To draw a graph for the given function and with the point
The solution for the given function f(x)=x+3 is
Given: Function is f(x)=x+3
To graph the given function.
Using the method of function.
The given function is f(x)=x+3
Now substitute x=2 in the given function,
f(2)=2+3
f(2)=5
Then the point is(2,5)
To draw a graph for the given function and the point is(2,5)
The solution for the given function f(x)=x+3 is
Page 72 Exercise 1 Answer
Given: function is f(x)=x+4
To find its range.
Using the method of function.
The given function is f(x)=x+4
substitute x=4
f(4)=4+4
f(4)=8
To find the function of
f(0)=0+4
f(0)=4
substitute x=2
f(2)=2+4
f(2)=6
The solution for the function f(x)=x+4 is
f(4)=8
f(0)=4
f(2)=6
Page 72 Exercise 2 Answer
Given: A function of “x” is given to us.
To find We have to find the function at x=−4,0,2
We will put the values of “x” in the given function and get the answer.
The given function is g(x)=5x
Putting the values of “x” in the given function, we get:
x=−4
⇒ g(−4)=5×−4
⇒ g(−4)=−20
x=0
⇒ g((0)=0
x=2
⇒ g(2)=5×2
⇒ g(2)=10
The values of the function at x=−4,0,2 are−20,0,10
Page 72 Exercise 3 Answer
Given: A function of “x” is given to us.
To find We have to find the function at =−4,0,2
We will put the values of “x” in the given function and get the answer.
The given function is h(x)=7−2x
Putting the values of “x” in the given function, we get
x=−4
⇒ h(−4)=7−2×−4
⇒ h(−4)=15
x=0
⇒ h(x)=7
x=2
⇒ h(2)=7−2×2
⇒ h(2)=3
The values of the function at x=−4,0,2 are 15,7,3
Page 72 Exercise 4 Answer
Given: A function of “x” is given to us.
To find We have to find the function at x=−4,0,2
We will put the values of “x” in the given function and get the answer.
The given function is s(x)=12−0.25x
Putting the values of “x” in the given function, we get:
x=−4
⇒ s(−4)=12−0.25×−4
⇒ s(−4)=13
s=0
⇒ s(0)=12
s=2
⇒ s(2)=12−0.25×2
⇒ s(2)=11.5
The values of the function at x=−4,0,2 are 13,12,11.5
Page 72 Exercise 5 Answer
Given: A function of “x” is given to us.
To find We have to find the function at =−4,0,2
We will put the values of “x” in the given function and get the answer.
The given function is t(x)=6+3x−2
t(x)=4+3x
Putting the values of “x” in the given function, we get
x=−4
⇒ t(x)=4+3×−4
⇒ t(x)=−8
x=0
⇒ t(x)=4
x=2
⇒ t(x)=4+3×2
⇒ t(x)=10
The values of the function at x=−4,0,2 are −8,4,10
Page 72 Exercise 6 Answer
Given: A function of “x” is given to us.
To find We have to find the function at x=−4,0,2
We will put the values of “x” in the given function and get the answer.
The given function is u(x)=−2−2x+7
⇒u(x)=−2x+5
Putting the values of “x” in the given function, we get
x=−4
⇒ u(x)=−2×−4+5
⇒ u(x)=13
x=0
⇒ u(x)=5
x=2
⇒ u(x)=−2×2+5
⇒ u(x)=1
The values of the function at x=−4,0,2 are 13,5,1
Page 72 Exercise 8 Answer
Given: A function of “x” is given to us. The value of the function is given at a certain “x”.
To find We have to find the value of x so that the function has the given value.
We will put the given value on the left-hand side of the given function and then solve the equation for “x”.
The given function is b(x)=−3x+1
Putting the given value b(x)=−20 in the above function and simplifying the equation for the value of “x”, we get
−20=−3x+1
−21=−3x
x=7
The value of x so that the function has the given value is 7.
Page 72 Exercise 9 Answer
Given: A function of “x” is given to us. The value of the function is given at a certain “x”.
To find We have to find the value of x so that the function has the given value.
We will put the given value on the left-hand side of the given function and then solve the equation for “x”.
The given function is r(x)=4x−3
Putting the given value r(x)=33 in the above function and simplifying the equation for the value of “x”, we get
33=4x−3
36=4x
x=9
The value of x so that the function has the given value is 9.
Page 72 Exercise 10 Answer
Given: A function of “x” is given to us. The value of the function is given at a certain “x”.
To find We have to find the value of x so that the function has the given value.
We will put the given value on the left-hand side of the given function and then solve the equation for “x”.
The given function is \(m(x)=\frac{-3}{5} x-4\)
Putting the given value m(x)=2 in the above function and simplifying the equation for the value of “x”, we get
2\(=\frac{-3}{5} x-4\)
6\(=\frac{-3}{5} x\)
x=\(=\frac{-30}{3}\)
x=−10
The value of x so that the function has the given value is−10.
Page 72 Exercise 11 Answer
Given: A function of “x” is given to us. The value of the function is given at a certain “x”.
To find We have to find the value of x so that the function has the given value.
We will put the given value on the left-hand side of the given function and then solve the equation for “x”.
The given function is \(=\frac{5}{6} x-3\)
Putting the given valuew(x)=−18 in the above function and simplifying the equation for the value of “x”, we get
−18\(=\frac{5}{6} x-3\)
−15\(=\frac{5}{6} x\)
x=\(-15 \times \frac{6}{5}\)
x=−3×6
x=−18
The value of x so that the function has the given value is−18.
Page 73 Exercise 13 Answer
Given: A linear function of “x” is given to us.
To find We have to complete the table and plot the points obtained on a graph.
We will put the values of “x” in the given function and get values of t(x)
then we will complete the table and plot the graph.
The given function is t(x)=1−2x.
Putting x=−4,−2,0, we get
x=−4
t(−4)=1−2×−4
t(−4)=9
x=−2
t(−2)=1−2×−2
t(−2)=5
x=0
t(0)=1−2×0
t(0)=1
Putting the values x=2,4, we get
x=2
t(2)=1−2×2
t(2)=−3
x=4
t(4)=1−2×4
t(4)=−7
The table that shows the value of the function at different values of x is given below
The graph of the linear function is given below
The table that shows the value of the function at different values of x is given below
The graph of the linear function is given below
