## 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)=x^{2}−1 Now to graph the equation

**The solution for the given expression h(x)=x ^{2}−1 is**

The given expression is j(x)=2x^{2}−3 Now to graph the given expression

**The solution for the given expression j(x)=2x ^{2}−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.

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